Absolutely, although not everyone in the NAS is going to know who you are if you call up as 'Bayflight', unless it's registered nationally.
As a Boston center controller, I can vouch that we have a way to look up callsigns in our database, but they have to be registered. Everytime a new callsign or a change of callsign is published, we receive a GENOT briefing item that we have to read prior to work.