If you had a time machine which would allow you to travel to the future (say, two-three years ahead of now) and saw the Bitcoins were universally accepted and dollar banned (Bitcoin addicts' pipe dream), would you spend your coins instead of dollars in the present?
Yes. Definitely. As soon as I got paid I'd immediately convert all my dollars into bitcoins. And when I had to buy something, I'd try to pay in bitcoins, rather than converting my bitcoins into dollars and then paying in dollars. The less time I have to hold dollars, the better. If I convert my bitcoins into dollars and then my dollars into food, I have to worry about the value of the dollar going down for the period of time I hold dollars. If I convert my bitcoins directly into food, then I eliminate this risk.
That's what Gresham's Law is about. You run away from a bad money (dollars) into a good money (bitcoins). If you are paid in dollars, you would then try to get rid of them as soon as possible, either through exchange for things or for bitcoins. So with that knowledge in your head you are first of all spending all your dollars...