I've played with a brace on my right wrist/thumb with no difficulties. In fact, it really helped out--I had the equivalent of carpal tunnel in my thumb. The brace gave good support and kept my thumb from hurting worse.
Can't say though how one on the left thumb would affect playing. I'd think it would hinder since you have to move that thumb.
I can say from my toe issues that if you can avoid fusing, DO SO!! Try all other options before going that route! Good luck with this.
Flutes:1975 Gemeinhardt M2 in chrome nickel;1982 Armstrong 80;2006 Yamaha 584
Piccs:1978 Artley piece of crap 15 P;1982 Gemeinhardt 4S;1980s? Armstrong all wood (no model)
Bass:2006 Jupiter di Medici G0199
Treble:2009 Guo New Voice
+ many flute-cousins