NASA has only contracted for flights with 4 astronauts, since the complement of the station is a maximum of 7 in the long term. The limit of 7 has many reasons, but some are for sleeping accommodations and life support systems capacity.
Soyuz can carry 3. Thus the current complement of ISS is limited to 6 (two Soyuz craft) at the moment.
Bringing 7 to the station would work in one flight of Dragon (or CST-100), if there were no Soyuz on station, but that is not a planned configuration. Could it happen? Sure. Anything could happen, but that is not the plan as currently set.
One possible case would be the direct hand-off. Lately, Soyuz flights have been doing indirect hand-off between missions. That is, a crew of 6 sends three home in a Soyuz, a week or three later another Soyuz launches with 3 more crew. On Mir, they would sometimes do it that way, but sometimes do it as a direct hand-off, where the new crew would launch on a Soyuz, the previous crew of 3 would be there, they would share the station for a few days to a week, then the old crew would depart. Sometimes they would change out the Soyuz, and the new Soyuz crew would leave on the old Soyuz to keep the on-station Sotyuz within its usage date. (Soyuz's in-space lifespan is 280-odd days.)
As a consequence, when shifting only 2 of the 3 crew members, there was room for a tourist.
With commercial crew (Dragon V2 or CST-100) there are more options.
With the current plan of 2 long-term stay (1 year) astronauts there are seats available for tourists on rotation flights.