Yes, you should be able to run the upgrade from Vista to 7 with an OEM disk. OEM copies are exactly the same as the full retail copies with 2 exceptions.
First, OEM copies only have either a 32 bit install disk, or a 64 bit install disk in the package (depending on which one you buy), but not both. Second, OEM licenses cannot be moved to a new PC if you upgrade your computer, or buy a new one. They must remain with the original PC you installed them on.