My DD is 14.5 weeks, what you do sounds similar. I always give DD a BF before bed, sometimes I am lucky and she'll fall asleep, other times I put her down and she'll seem content but in 5 mins crying.
The thing we listen for is the type of crying if its a "I'm tired" cry we leave her to wind down but if its a "I'm upset and need a cuddle" cry we go straight into her. I then usually will try to settle her in the cot first, if that doesn't work I will give her a cuddle til she's drowsy and if that still doesn't work I give her the boob again.
As you asked about if its okay to leave a baby to cry at all well as I said above I think it depends on the type of cry. I don't think the tired cry is causing any distress to my DD cause she looks half asleep when she does it and her body language doesn't seem to be upset but anytime she starts getting upset I go to comfort her. Personally I don't see how babies who are left to cry when distressed can peacefully fall asleep, I know if I'm really upset there is no way I could sleep unless calmed down first. Its like Cailin said, "We believe in comforting a child rather than leaving them to cry".
And as dachlostar said a few mins wouldn't hurt. Sometimes you need to get something done or I know sometimes when a baby cries on and on you need to put them down for a few mins for your own sanity.