At first I thought this was going to be a suggestion for a repair structure for Terran. There is no cost for lowering supply depots as I know it. But I don't think it's been mentioned before.
However, you might need to research it first which would cost you resources. I mean it would make sense to make it an upgrade - you could either go defensive and research it early on and build them accordingly or go offensive and not bother with supply depot barriers. Yeah... that makes sense, I like it ;D
What about supply? Does it temporality take away from supply (possible delaying production) if you have them lowered?
I don't think so. If it's up no one can pass, if it's down everyone can, it should be as simple as that imo
Dustin (or some other blizzdood) confirmed that it doesn't take away supply. But we don't know if it has to be researched.