Yes, you can. You do this by using the mount command. For example, if you plug in the thumbdrive and dmesg says it was detected as 'sdb', you would:
Create a mount point:
Mount the drive:
mount /dev/sdb ./thumbdrive
You may also want to consider using the Fedora 7 LiveCD. You can use that as a rescue disk, and it gives you access to your full GUI environment.