modifying a gerund with a counterfactual if-clause

If is a conjunction like and, or or but. It typically conjuncts two clauses.

That's what's happening here.

[clause 1]:{ I like the idea of buying a castle } if [clause 2]:{ I were a billionaire }.

Clause 2 is not modifying clause 1 or anything in it. The entirety of "I like the idea of buying a castle" is something that depends on condition "I were a billonaire." Nothing in "I were a billonaire" connects back to anything more specific than that.

Now, written like this I think it's closer to what you are talking about

I like the idea of buying, if I were a billionare, a castle.

but this only works with clear pauses/intonations in speech and commas in writing. So I think this is something like a parenthetical structure, and again not a direct modifying relationship.

The expression
*I like the idea of buying a castle if I were a billionaire.
is not correct. It has nothing to do with whether a gerund is involved, so let's leave it out.

*I like the idea if I were a billionaire.
is not correct.
This conditional sentence has to use "would". The following is correct:
I would like the idea if I were a billionaire.

Now that the structure is valid, the original expression is
I would like the ides of buying a castle if I were a billionaire.

I think I misunderstood the OP. Thanks to Gary and Apollyon for clarifying it for me. The question is, is the following expression, with a conditional modifying a gerund, valid:
the idea of buying a castle if I were a billionaire

I'm not at all sure. Is the following a valid sentence?

The idea of buying a castle if I were a billionaire appeals to me.

I think the original post's sentence sounds wrong, because the entire sentence sounds like a conditional, but put this way, I'm not sure.