Normally, Link isn't able to move at all when there are strings on screen. Though, I hope it's possible to allow Link to move around on the screen while also having strings play at the same time. It's kind of like having the "Messages Freeze All Action" rule unchecked, but instead of still having Link frozen in time, Link is able to move.
I hope this is enough information, and if it isn't, I'd be glad to clear up anything.