Be careful if you try to do this -- it is in theory possible but if you accidentally cross certain one-way boundaries (e.g. customs, and maybe immigration as well), you will not be able to enter the A pier without a boarding pass for a flight departing from one of those gates.

I've never tried to do this since I'm BRU-based and therefore always originating or ending here, but next time I'm through there I'll try to snoop more thoroughly and report back on whether this is possible. As an aside, though, the SN lounge dragons are among the more strict and may decline you entry and send you back to the B pier and its lounge.