You need good 3D acceleration for most modern desktops to work fast and
smooth. Fallback mode of Gnome 3 (which is the standard for Trisquel anyway)
seems to work without 3D acceleration but you would still want good 2D
acceleration for everything to be smooth and not CPU heavy, but even that is
subpar with many Radeon cards.
That's the dilemma nowadays, you either have a free BIOS, but lacking support
for the GPU, or your GPU is supported very well but then you have a non-free
BIOS. I've gone the second route, because in everyday work the non-free
graphicsdriver poses more of a problem than a non-free BIOS.
As Chris said, it is theoretically possible to build a system with a free
BIOS and one of the NVIDIA cards that work well with the reverse engineered
nouveau driver. That would be the closest you can get to a fully free system
nowadays, but you'd be supporting NVIDIA with your purchase, while NVIDIA has
been kind of an ass to the community...
There is no perfect solution right now, good luck at getting it as far as you
can get and having a solid environment!