If you are departing a MF aerodrome with an active FSS...with the visibility at say 2 SM... If you request special VFR for departure.. Can you pickup your filed IFR clearance airborne to save time on the ground?

You are unlikely to get your special VFR clearance any faster than your IFR clearance. Plus it's not a great idea to depart in marginal VFR conditions hoping that you can stay VFR and get high enough to get your IFR clearance. A good tidbit of advice I got early in my career: "It's an IFR airplane. Go IFR"

But yes, what you describe is perfectly legal, as long as you can climb to a safe IFR altitude VFR.

At some FSS they do have local agreements with the regions centre controllers letting them approve SVFR. At those units it would be fast to depart. I do agree with the above post about IFR flight. You may depart faster but there's no telling when you'll be able to get your IFR clearance.