I recruited them to help me in the project.
Is it possible to say and mean the same thing?
To help me in the project, I recruited them.
Your rewrite is grammatical, but it is unlikely that a native writer would use it.
This is not a matter of idiom, but of “information packaging”. Usually the “new” and therefore most important information in a sentence falls in the predicate—usually the verb and its complements or sometimes a closing adjunct which adds information about the predicate. For instance: in your first sentence the personal pronoun them has to refer to something earlier in your discourse; you have already inroduced or called attention to them; so the new information is presumably the fact that you recruited them and why.
The two gentlemen on the platform are John Doe and Richard Roe; I recruited them to help with the project.
But in your second sentence, them occupies the strongest possible position: it is the final word of the sentence and of the very short main clause. Them almost has to be the new information; and yet it refers to people already introduced. We have to strain to invent circumstances in which this would be natural. Perhaps them is used emphatically, as a demonstrative rather than a personal pronoun; think of this as a stage play:
M: To help me in this project I recruited— (pointing) them!
(The doors are flung open to reveal John and Richard. The assembled journalists applaud wildly.)