Ahem...
When I first used Trisquel, I added on proprietary software to it. I won't
name the particular program I'm thinking of, but I will say that it was a
game. Additionally, my brother had no trouble whatsoever installing a
proprietary Web browser onto one of my mom's computers (with her
authorization). So, no, Trisquel doesn't prevent you from installing
proprietary software.
How would Trisquel even do that, anyway? Short of being designed to refuse to
connect to any resource on the Internet without special approval by some
authority?