Absolutley not, most people that have 6.1 or 7.1 hardware only are connecting a 5.1 system because of the additional expense, complexity and logistics of adding the additional hardware. The bottom line a 5.1 setup will be just fine and leave you head room to upgrade to a 6.1 or 7.1 system when you are ready.
My previous and current receiver are/were 6.1. I ran 5.1 with my previous setup and was very happy with it, but for one of the reasons Roger lists, I do not run 6.1 in my current setup (no place for a rear center). You simply tell the receiver you do not have a rear center. You will not be "missing" anything, all the sound will be processed normally, even when listening to 6.1 tracks. You will be hard pressed to find a decent receiver these days that isn't at least 6 channel.