My opinion is no. Reason is because if someone hires a private investigator early on, there's a trust issue; definately not worth fighting for, until someone knows the cold hard facts straight from the horse's mouth. Or the horse's partner... If there are doubts at the beginning / after a few dates, why bother going through dating that person? Dating is a "getting to know each other process".
The only reason I would hire one (private investigator) would be if I'd be in a longterm relationship, and suspect that I'm being cheated on, or that my partner might be implicated in some criminal activity...who knows? Then, I would certainly want to know for sure and not assume something is going on. Then I would proceed with separation or divorce, whatever the case would be.
However, if I'd be in a relationship say, anywhere from three to six months or something like that, and trusted friends would try to warn me that this individual has a very shady past, as hard as it might be, love would not stand in my way. I would tell the person about what I'd just heard, I would put an end to that relationship. I would not take any chances. Trusted friends would not want to hurt a friend's feelings by telling lies or starting rumours. Friends want what's best for us; usually.
So sum it all up, you did the right thing by putting an end to it.

Readybake101: Would you hire one to check out a new mate after say 3 or 5 dates and why? Do you really want to know his record with women or vice versa?
I dated a well divorced church goer. Lo and behold if his last wife did not contact me .. she was alright .. told me all the gritty stuff about him .. but needless to say I can't be bothered with him anymore.