Yes, they can. It is reasonable to think that the sentence is a cleft sentence without the subject part.
The basic pattern will be XのはYだ/です, where X is a sentence and Y is a phrase. In your case, it should be something like
- It is by the 勢い of being drunk (that I said such a thing).
Note () part is just what I guessed, it should be replace as appropriate to the context.
Similarly, other particle+だ are possible. A bit artificial example:
- 彼はあなたに花を贈った He sent you flowers.
- 彼が花を贈ったのはあなたにだ It was to you that he sent flowers
In case of を or へ, I suppose it is more common to drop the copula in the sentence like the example:
- 何を見てるんですか What are you watching?
- 歩いている人をだ. (It's) Walking people (that I'm watching).
Here colloquially だ and even を would be dropped (=歩いている人).