No. Standard USB floppy drives contain a separate floppy controller chip, which is not directly accessible from the host PC. Without that access it’s not possible to support formats beyond what the drive chooses to expose (usually 720K and 1.44M formats only).
However, there are a number of advanced USB-based floppy projects in development, which give extremely low-level access to floppy media. Support for such devices will be considered in the future.
Most PC-compatible soft-sectored disks should work, without prior knowledge of the format. If there’s an existing DOS/Linux utility for them, you should have no problems. If in doubt, scan the disks and see what shows up.
The PC floppy controller is quite limited compared to some other chips (particularly the WD17xx) and full track-level control. Consequently, there are problem areas that cannot be supported:
Probably, but only for basic reading and writing tasks. Core functionality remains higher priority than a GUI, so advanced features are likely to remain command-line only.
Yes, but initially supporting only disk image and hard disk functions.
Limited floppy access may be added to Linux later, using the fdrawcmd ioctl interface. It lacks the special short-write functionality provided by fdrawcmd.sys, and without it the following can’t be written correctly:
Looking further ahead, these may be supported on all platforms using flux-level USB devices such as the KryoFlux and DiscFerret.