Xilinx, Altera and Lattice use Qt already. The bigger problem is supporting all the hardware debuggers and programmers.
This shouldn't be a problem at all -- Silicon Labs' USB programming dongles all work on all three platforms. Segger provides drivers for all three platforms and I used the GNU-Eclipse-GCC-whatever setup on my Mac for an Atmel SAM project, and the debugger/programmer worked flawlessly. I think NXP's stuff was all cross-platform, too, but I have not kept up with it.
And at least for Xilinx Linux (or UNIX, I guess) support was there first or at least from early on. Since some of the tools in ISE are still using Tk.
Xilinx supported high-$$$ Unixes like HP-UX and IBM's flavor from basically the beginning (I remember X Windowing into a Unix server from an NT box in 1996). It took them forever to support Linux, and as I remember they finally came on board with Linux in 1999 or 2000. And now I remember them supporting Solaris; at one job we had Solaris servers that we'd use for the big runs.