Yes, USB->VGA boxes contains a full graphics card with memory and all, so you can use them with any hardware capable of sending out the USB information. There may be different ways to implement them, but the ones I have played with have had a USB controller that have allowed the USB host to send data to either image memory or to registers in the unit.

Depending on the speed of the USB interface (especially if the host side can't do 480Mbit), you will have a hard time creating fast animations. But you can normally draw the next image into a separate memory page and then instantly swap from one image to the next. For a specific project, a slow 48MHz 32-bit processor using 12Mbit USB, managed a number of frames/second.

I can't of course prove that all USB graphics cards will work well (or at all) with 12Mbit USB, but if the specific unit doesn't have such a limitation, just about any 8-bit processor with a USB host controller should be able to produce usable static displays. The current time of day (maybe not with seconds or flashing colon), menu information, number of places left in a parking lot etc.

It helps a lot of the processor isn't too RAM-starved, since even low-resolution modes represents a lot of data when running in graphics modes, and in graphics modes the processor will have to care about characters and memory blocks. Trying to send the data one pixel at a time is too slow, so the program should be able to draw the data in blocks and transfer the blocks to video RAM.