If by OEM, you mean Dell or HP etc there will be a problem. On the hdd is a full system restore, usually on D: partition. If Op has a x86 original system, then upgrades to x64, the system restore will conflict. OP would not only have go do a full clean install which is only a format of C: but a repartition, to erase D: and allow a clean system restore to be installed on a newly created D:
There is of course no guarantee that the key will work on the new OS. Being OEM, the key is integrated with the motherboard, its proprietary to that OEM. Best bet would be to contact the OEM support, and get a copy of x64 Windows from them, or at minimum, verify that a public x64 version will be compatible with the OEM key.