You can mount a foil on just about any board you'd like really. It's just a matter of having a board strong enough and a strong enough mounting system for it.
Some of the boards these guys use look just like twin tips to me. Of course you wouldn't be able to use your TT straps since foils are directional... so either go strapless or put maybe one bi-directional strap for the front foot at least. You could stick surfboard pads on top or make some kind of grippy surface.
It could be a good project if you have a TT that would otherwise go to waste. The other challenge is finding the right position to mount it under the board, I'm sure others on this forum could advise you with this.
Christian