Will a .ino Arduino Sketch compile directly on GCC-AVR?

See my answer here: Classes and objects: how many and which file types do I actually need to use them? - specifically: How the IDE organizes things.

I know that at a minimum you have to include the Arduino header file

Yes you would need to do that.

but beyond that, what would cause a compilation error if compiling said .ino to .cpp file using, say, for instance GCC-AVR.

The IDE generates function prototypes for you. Code in a .ino file may or may not need this (it probably will unless the author is disciplined enough to code in the usual C++ way and do them themselves).

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If the "sketch" contains other files (eg. other .ino, .c or .cpp files) then these would need to be incorporated in the compile process as I describe in my answer mentioned above.

Also you would need to (compile and) link in any libraries used by the sketch.

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You haven't asked about the linking side of things, but naturally the various files, as compiled, need to be linked together, and then turned into a .elf and .hex file for uploading purposes. See below.

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Example makefile

Based on the IDE output I made a simple makefile a while back:

#
# Simple Arduino Makefile
#
# Author: Nick Gammon
# Date: 18th March 2015

# where you installed the Arduino app
ARDUINO_DIR = C:/Documents and Settings/Nick/Desktop/arduino-1.0.6/

# various programs
CC = "$(ARDUINO_DIR)hardware/tools/avr/bin/avr-gcc"
CPP = "$(ARDUINO_DIR)hardware/tools/avr/bin/avr-g++"
AR = "$(ARDUINO_DIR)hardware/tools/avr/bin/avr-ar"
OBJ_COPY = "$(ARDUINO_DIR)hardware/tools/avr/bin/avr-objcopy"

MAIN_SKETCH = Blink.cpp

# compile flags for g++ and gcc

# may need to change these
F_CPU = 16000000
MCU = atmega328p

# compile flags
GENERAL_FLAGS = -c -g -Os -Wall -ffunction-sections -fdata-sections -mmcu=$(MCU) -DF_CPU=$(F_CPU)L -MMD -DUSB_VID=null -DUSB_PID=null -DARDUINO=106
CPP_FLAGS = $(GENERAL_FLAGS) -fno-exceptions
CC_FLAGS  = $(GENERAL_FLAGS)

# location of include files
INCLUDE_FILES = "-I$(ARDUINO_DIR)hardware/arduino/cores/arduino" "-I$(ARDUINO_DIR)hardware/arduino/variants/standard"

# library sources
LIBRARY_DIR = "$(ARDUINO_DIR)hardware/arduino/cores/arduino/"

build:

    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(MAIN_SKETCH) -o $(MAIN_SKETCH).o
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)avr-libc/malloc.c -o malloc.c.o 
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)avr-libc/realloc.c -o realloc.c.o 
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)WInterrupts.c -o WInterrupts.c.o 
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)wiring.c -o wiring.c.o 
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)wiring_analog.c -o wiring_analog.c.o 
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)wiring_digital.c -o wiring_digital.c.o 
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)wiring_pulse.c -o wiring_pulse.c.o 
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)wiring_shift.c -o wiring_shift.c.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)CDC.cpp -o CDC.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)HardwareSerial.cpp -o HardwareSerial.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)HID.cpp -o HID.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)IPAddress.cpp -o IPAddress.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)main.cpp -o main.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)new.cpp -o new.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)Print.cpp -o Print.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)Stream.cpp -o Stream.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)Tone.cpp -o Tone.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)USBCore.cpp -o USBCore.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)WMath.cpp -o WMath.cpp.o 
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)WString.cpp -o WString.cpp.o 
    rm core.a
    $(AR) rcs core.a malloc.c.o 
    $(AR) rcs core.a realloc.c.o 
    $(AR) rcs core.a WInterrupts.c.o 
    $(AR) rcs core.a wiring.c.o 
    $(AR) rcs core.a wiring_analog.c.o 
    $(AR) rcs core.a wiring_digital.c.o 
    $(AR) rcs core.a wiring_pulse.c.o 
    $(AR) rcs core.a wiring_shift.c.o 
    $(AR) rcs core.a CDC.cpp.o 
    $(AR) rcs core.a HardwareSerial.cpp.o 
    $(AR) rcs core.a HID.cpp.o 
    $(AR) rcs core.a IPAddress.cpp.o 
    $(AR) rcs core.a main.cpp.o 
    $(AR) rcs core.a new.cpp.o 
    $(AR) rcs core.a Print.cpp.o 
    $(AR) rcs core.a Stream.cpp.o 
    $(AR) rcs core.a Tone.cpp.o 
    $(AR) rcs core.a USBCore.cpp.o 
    $(AR) rcs core.a WMath.cpp.o 
    $(AR) rcs core.a WString.cpp.o 
    $(CC) -Os -Wl,--gc-sections -mmcu=$(MCU) -o $(MAIN_SKETCH).elf $(MAIN_SKETCH).o core.a -lm 
    $(OBJ_COPY) -O ihex -j .eeprom --set-section-flags=.eeprom=alloc,load --no-change-warnings --change-section-lma .eeprom=0 $(MAIN_SKETCH).elf $(MAIN_SKETCH).eep 
    $(OBJ_COPY) -O ihex -R .eeprom $(MAIN_SKETCH).elf $(MAIN_SKETCH).hex 

In that particular case, the .ino file compiled without any problems after renaming it to Blink.cpp and adding this line:

#include <Arduino.h>

I would just like to add a few points to Nick Gammon's answer:

• You do not need to rename a .ino file in order to compile it: if you explicitly tell the compiler it's C++ (option -x c++), it will ignore the unusual file extension and compile it as C++.
• You do not need to add #include <Arduino.h> in the .ino file: you can tell the compiler to do that for you (-include Arduino.h).

Using those tricks, I can compile Blink.ino with no modification, just by invoking avr-g++ with the proper command-line options:

avr-g++ -mmcu=atmega328p -DARDUINO=105 -DF_CPU=16000000L \
    -I/usr/share/arduino/hardware/arduino/cores/arduino \
    -I/usr/share/arduino/hardware/arduino/variants/standard \
    -Os -fno-exceptions -ffunction-sections -fdata-sections \
    -Wl,--gc-sections -g -Wall -Wextra \
    -x c++ -include Arduino.h \
    /usr/share/arduino/examples/01.Basics/Blink/Blink.ino \
    -x none /usr/local/lib/arduino/uno/libcore.a -lm \
    -o Blink.elf

A few notes on the above command-line:

• /usr/local/lib/arduino/uno/libcore.a is where I saved the compiled Arduino core. I hate recompiling over and over again the same stuff.
• -x none is needed to tell the compiler to mind the file extensions again. Without it, it would assume libcore.a is a C++ file.

I learned those tricks from Sudar Muthu's Arduino-Makefile. This is a very general Makefile that works with many boards and with libraries. The only thing missing relative to the Arduino IDE is the forward declarations.