Support for USB controllers in DOS and Win3.1 is, of course, basically nonexistent. However, with the correct BIOS settings, a USB storage volume can be treated as a conventional hard drive (naturally requiring a traditional, non-GPT partition table, and will only mount sub-2GB FAT16 partitions).
I've got a bootalble thumbdrive, in fact, set up with Syslinux, and an option to boot a DOS 6.22 drive image (with Win3.1 installed) via memdisk. It works, but on modern hardware, can typically only use standard VGA or VESA video modes, and modern HDA audio devices are usually not AC97 or SB compatible, so usually no audio but PC speaker.