Does it get light early enough to motor from Norman to Sopers to make a 7:30 am ferry?

I think yes - are you just bringing someone over for the ferry and going back? I'm guessing yes...since I highly doubt anyone would be at the Voyage base to check you back in <img src="http://www.traveltalkonline.com/forums/images/graemlins/Laugh.gif" alt="" /> that early....

If you have to be there by 7:00-7:15, then you are pushing it. Are you in a power cat or sailboat? We've done Nanny Cay at that time in the morning. But, I'm guessing you're looking at ~ 8 nautical miles. You might want to spend the night at an outer mooring ball (Bight). Maneuvering through the mooring field can be a challenge in nautical twilight. It can also hurt your popularity with those sleeping on other boats.

We will be dropping 2 people off, then waiting for 3 coming in on the first ferry.

We will be on a 46' Leopard

Agree with being outer ball. Up early and should be able to leave at first light.
Sunrise (weather .com) shows 06:11 sunrise currently. Usually civil daylight is 30 min before then and potentially enough light for you to leave earlier. I would feel comfortable leaving in dark with my chartplotter.
One other consideration is whether your contract forbids movement at certain times.

Seems like a very tight window.

Kevin

If you motor over it will take one hour. Get underweigh about 5:45 am and you will be fine. You might not get a ball in Sopers until 8 or so when people start leaving so plan on hovering the boat to run them in.
A simpler alternative would be to simply spend the night at Sopers. It's a not a bad place to stay.