depending where you are, it probobly won't save time. i live in lyons and it takes me the same amount of time to get to pumphouse weather i go through the park or down to I 70. if you're in or around denver, take i-70.
you can drive through any time, but it costs $15 or $20 if you don't have a parks pass. plus there is a VERY good chance the road will be shut down tonight. they closed it last night, it reopened late morning. it will suck to get up there and find it closed. been there myself. hope this helps.
just saw your in FC. i don't thimk it would save you much, but it would be a little quicker. still i wouldn't risk it being closed. you can call the park 303-586-2371 to find out before you head out . good luck.