Applying for citizenship is only the beginning of the process. Doesn't the process have to complete, up to and including being sworn in as a citizen, before you can call the person a citizen?
-PJ
Yes. Naturalization as a process takes a while.
Then, to serve in Congress, one must have been a citizen for seven years.
See the U.S.Constitution: Article I; Section 2; clause 2.
Unlike other nations, we do not bar naturalized citizens from participating in elective office.