Possibly. The text of the actual NATO treaty is quite short and accessible. There is no article requiring the removal of a state that annexes or invades a neighbor. In fact, there's no expulsion language at all. But the general understanding when enacted was the lack of an expulsion clause wasn't an issue, as any state that failed to live up to the ideals set up in Article 1 and 2 could be declared in material breach of their treaty obligations:
Article 1 The Parties undertake, as set forth in the Charter of the
United Nations, to settle any international dispute in which they may
be involved by peaceful means in such a manner that international
peace and security and justice are not endangered, and to refrain in
their international relations from the threat or use of force in any
manner inconsistent with the purposes of the United Nations.
Article 2 The Parties will contribute toward the further development
of peaceful and friendly international relations by strengthening
their free institutions, by bringing about a better understanding of
the principles upon which these institutions are founded, and by
promoting conditions of stability and well-being. They will seek to
eliminate conflict in their international economic policies and will
encourage economic collaboration between any or all of them.
After the dissolution of the USSR, NATO also set out a "Membership Action Plan" that prospective members would have to meet in order for their application to NATO to be approved. The five major requirements are:
--New members must uphold democracy, including tolerating diversity.
--New members must be making progress toward a market economy.
--Their military forces must be under firm civilian control.
--They must be good neighbors and respect sovereignty outside their borders.
--They must be working toward compatibility with NATO forces.
Technically speaking, these are only requirements for entering NATO, not ongoing membership, and they were only laid out after Poland had already joined. But in combination, there is a strong assumption that NATO members act and look a certain way. Even if Poland's annexation was bloodless and done in a bare democratic fashion, it would pretty clearly be in violation of NATO's general request that members act like good neighbors and promote regional stability.
The question would then become whether other NATO members actually feel obliged to press the issue or look the other way (as they currently do for a lot of Turkey's bad behavior). Unlike the democratic ideals promoted by NATO, the "good neighbors" expectation is also one of practicality. NATO is obligated to come to the defense of Poland if they are attacked, the expectation from other NATO states is that Poland in return should not be out there provoking conflict with its neighbors and forcing them into unnecessary and unjust wars.
The thing to keep in mind here is treaties are only as strong as the will to abide by them. The text of the NATO obligations could be clear cut in Poland's favor, but if the other NATO states don't want to come to Poland's aid, the international treaty police are not going to show up and make them. If Poland says "We're in NATO," and every other participating nation says "ah, but we'd prefer if you weren't," practically speaking, Poland is not in NATO any longer and the question if they legally are is entirely academic.