It depends on what you mean by "conceive" and "thought experiment." If the thought experiment can be expressed, you can come up with a word to describe the expression of the idea. I think I could imagine some inexpressible ideas (this seems like it would logically follow from the proof that some things are not computable.)
Of course, when you deal with real language your language itself is constrained. If you need to invent a bunch of new words does that count?