That is possible. Just keep in mind that you won't be able to use the grill below the pig while roasting a pig. The heat requirements are different. For the pig you want a nice steady temp around 200-250 degrees for between 6 - 12 hours (depends on the size of the pig, you keep roasting till you hit an internal temp of 160-165 in the ham)
For grilling burgers and such you want a temp at the grill level of closer to 300-400 degrees, higher if you want the initial turns to exhibit grill marks.
For roasting you want the heat 14" or more away from the meat, With a drip pan between them to avoid fires and the burnt fat taste. For grilling you want 6-8" between the fire and meat.
Most big pits have a small grill added to the side to do the burgers and such. Mine started life as a 500 gallon round tank. It has a propane burner bar down each side that allows me to start a fire in it easily. It also allows the temp to be controlled MUCH easier. For the main fuel source I use either good dry hardwood (Maple, Beech, Ash) Or good charcoal. The pit has a rotisserie powered with a 1 HP gear head motor. Turns the spit at just under .75 RPM. I built it to handle pigs/beef up to 300 - 400 pounds I attached a grill to the side that also uses propane/charcoal to do burgers/steaks and such. Also have a deep fryer and pair of top burners to make sauces/cook corn or whatever else.