No. You need to report all income received in the tax year from all sources on one tax return. So you have to wait for that other W-2, along with any other tax reporting documents that may be coming your way. The deadline for most tax reporting documents (like W-2 and 1099-MISC) to be in the mail is Dec 31. So it's perfectly possible you won't have that W-2 until close to the end of the first week of Feb.
