Yes, but the Constitution specifically required the consent of Virginia. At least if Virginia was still a state.
"Section 3 - New States"
"New States may be admitted by the Congress into this Union; but no new States shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress."
And as I pointed out, the body of the Virginia legislature that remained loyal to the Union and which was recognized by the Congress as the legitimate legislature of Virginia did vote to partition the state. The letter of the law was followed if, perhaps, not the spirit.
FWIW Lincoln had his doubts on the legality of West Virginia's admission but the president has no constitutional role in admitting a state so there was nothing he could do about it.