Since OP has an 03 chances are he doesn't have any seat mounted side airbags. You can check if you do by looking on the outside front seat bolsters, if you have a tag saying something like "SRS Airbag" then you got 'em.
Removing the seat doesn't deactivate the whole system, the light lights up to tell you that something is wrong with the airbag system, not to tell you that the airbags are deactivated. In the case of a crash my guess is the passenger airbag won't go off at all because the system isn't getting a reading from the seat weight sensor. I wouldn't be worried, OP. :thumb: