Had he merely stated it as a conjecture without claiming that he had proven it, would anywhere near the same effort have been put into proving it?

Almost certainly not. A lot of the historical interest came precisely because he claimed to have a proof. In fact, there were a fair number of occasions where he claimed to have a proof and a decent chunk of number theory in the 1700s and early 1800s was finding proofs for the statements that Fermat had said he had a proof for. It was called "Fermat's Last Theorem" because it was the last one standing of all his claims.