I booked SN only itineraries on united.com without any problem, and to my recollection they allow for a free checked bag. If you really want to be sure, look at your itinerary on the united website. Does it say 'Additional Information" or something similar near the top? If so, click that and you should get the SN confirmation number. Take that the Brussels Airlines website and check your reservation. This will tell you what type of fare you have.

If your itinerary doesn't display the SN PNR, you can get it by calling United.