Can the Arduino interface with USB devices without the USB host shield?

First things first you need to learn the basics of how USB works.

In USB there are two main "things": Hosts and Devices.

You have one Host (usually your computer) and many Devices (such as Arduinos, Printers, Scanners, Webcams, WiFi dongles, etc).

Being a host involves knowing about what devices you are going to have attached to you and how to communicate with them. Being a device means just communicating with the host in your own way.

As you can see it is a far more complex job being a host than being a device.

Arduinos are devices. The small USB interface chips they use are very low powered and can only be a device, never a host.

If you want to plug a device into something it has to be a host (note: I am purposely ignoring hubs here).

The Arduino Due uses a far more powerful chip, and that is capable of being a host (using what is known as On-The-Go mode).

To do it with anything less powerful than a Due you require additional hardware that is specifically designed to be a USB host - and that is where the USB host shield comes in. It has a chip that is designed specially to be a USB host so you can plug a device in to it.

None of the chips on the Uno are designed to be a host. They just don't have the power.

No. USB strictly distinguishes between host and device roles. A few chips have functional blocks capable of performing either role, but the 8u2/16u2 are not examples of this.

Typical USB serial converters like the FT232, CP210x, CH340, PL2303, etc are also strictly devices and incapable of being hosts

There are inexpensive host-capable MCUs like the Kinetis KL25Z, but to use them in their cheapest form you would need a different software approach (for example mbed rather than Arduino) and a lot more personal effort. The Teensy-LC is related, but you pay more for the Arduino code loading helper on it than for the MCU that runs your program itself.