It will run but slower. I find it best to have all programme files on your main computer hard drive, then pictures, music, videos etc on a secondary hard drive.
I remember when at uni, even though I had USB 2, it was quicker to transfer files through the network via ethernet cable rather than having a hard drive plugged in via USB.
So I just used to go upto my mates room who always had his PC open due to cooling issues and used to plug my hard drive into his computer and transfer large files that way.