Bharat,
I felt a little apprehensive about my (now) husband and son traveling alone, too. It was their first trip overseas and first big jet trip, too. I felt better traveling there, spending a little more time getting to know more of his family, and traveling with my (then) fiance and son to the US. With changing planes and a long layover in Bangkok, I think it was definitely the right decision. At the POE (JFK) I asked the roving officer if I could go with them into the non-citizen line and he seemed fine with that.
It was really fun and interesting seeing their reactions to things along the way, too.
I'll bet your fiancee would be relieved and happy to have you by her side during the trip and at the POE.
Best wishes, whatever you decide, and congratulations!
Maya