Absolutely you can do this, I've done it several times. You do need to show the baggage stubs in SIN when checking in for that last SIN-XXX leg, at least I did. No big deal since you're getting your Boarding card there anyway.

It's a mixed bag whether the agent in BOS will even ask to see your SQ ticket or itinerary. I've usually showed it just to make sure they get it right on the baggage tag.