Does USB Host always supply power on VBUS?
A standard classic USB host must always provide VBUS (+5V +- 10%) to a downstream port, so a device can initiate the connect sequence (pull D+ or D- high). The port must provide at least 500 mA (2.0 version) or 900 mA (3.0 version), regardless of whether there is any communication or attachment or else. These are "at least" requirements for classic USB 2.0 and USB 3.0 "high-power ports" and powered hubs, so they can supply more if they wish. The requirements are listed in Section 7.2 of USB 2.0 Specifications. Small battery-powered might have an exception.
NOTE1: VBUS must be supplied by host even in "sleep" (suspend state) mode.
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NOTE2: if a host doesn't drive VBUS high, no attachment would/should occur, even if the device has own power. Connect requests (D+ or D- pull-ups) must occur only if VBUS is present, by USB 2.0 specifications Sec.7.2.1. So it is a spec violation just to "have" the pull-ups, the pull-up must be conditional with VBUS.
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NOTE3: So, no VBUS => no communication. Becuse of this rule, no "partial" or "host-signaling" mode is possible without VBUS.
The 500 mA is a requirement for USB HOST. This supply number is frequently confused with a requirement for a USB DEVICE as consumer. A USB device SHOULD NOT draw more than 100 mA upon initial connect stage, and can draw full power only when it gets enumerated and receives "set_configuration ()" command. USB devices report their power requirements in device descriptor, during this inital "100mA" session. If the host has exhausted its power budget, it can stop the enumeration, effectively rejecting the device.
NOTE4: as one can see, there is no "negotiation", it is either "my [host] way", or "freeway".
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NOTE5: USB hosts have no specified means to police actual power consumption from its ports. USB host controllers don't have any registers that can measure/report ports consumption. Therefore a host cannot enforce the 100mA limit to police out bad devices that might violate the 100 mA specification, unless a drastic event of port overcurrent occurs. The compliance to 100 mA limit was thought at the level of USB-IF certification process.
In short, the 500 mA and 100 mA are requirements for different USB entities, one for hosts and hubs, and another for devices, again as described in Section 7.2.1. This is how it works from USB standard point of view.
Now things are a bit different with introduction of Type-C connector. Type-C devices (both hosts and peripherals) are prohibited to output VBUS, initially. So, instead of boldly having VBUS power on a Type-C port, the host must turn on VBUS source only if the port logic detects the presence of cable/device. It does this by sensing voltage level on "CC" (Communication Channel) pin. A Type-C host has a pull-up on both CC pins. A device (or legacy cable assembly) must have 5.1k pull-down. When device/cable is plugged in, the host detects that 5.k drags its pull-up down, and at this point the host has rights to engage VBUS power, and USB communication begins.
Unless it is in some sort of sleep or overcurrent fault mode, yes, an ordinary (Classic 1.0/1.1/2.0) USB host would always supply power to VBUS.
USB devices are detected by the host because they have a pull-up resistor on one of the data lines - D- for a low-speed device, and D+ for a full speed device (or a high speed device; the high speed is discovered in the signalling).
While the USB spec prohibits peripherals from drawing more than 100 mA without negotiation, in practice many (most) hosts do not enforce this. Typically they have some kind of PTC or active overcurrent protection which kicks in somewhere above 500 mA (a few, like original Raspberry pi's had lower limits, and could not source full USB spec current).
A few early smarthphones had non-compliant partial USB host capability, they were able to operate in the host signalling role, but not source VBUS to a peripheral. Most today either have a charge pump to supply VBUS or do not permit host mode operation at all.