Yes, sketchup is free.
Yes, you can do what you want with it.
Yes, there is a learning curve, but it isn't nearly as steep as several other apps.
Will it be faster? Probably not for you since you're so used to Corel, i have to imagine. That's a tough one for us to really answer since it's so subject to personal style.
I'd hate for you to have a deadline looming and tainting your impression of SketchUp, though. Might be good to save learning it for a rainy day when you have no particular pressure. At least for me, if i had trouble trying to get a simple thing done and i didn't have the time to meander through it at a leisurely pace, i'd get frustrated by every hurdle and not look kindly on the software.