Not if you're terminating at SIN. The SQ lounges are strictly departures lounges, where it's understood that the term departures in this context includes connecting passengers.

If you really want an arrivals lounge, one option is to book (and pay for) Jet Quai service.

If you're a PP member, there *might* be a new land side PP lounge at SIN, which would require a same day boarding pass but not a departure from SIN. Check the PP website for location and other details. Otherwise AFAIK all of the pay lounges at SIN are airside and probably would not let you purchase entry without a departing boarding pass, but you might want to check their rules (I assume they're posted on some website) to be sure.