The effect of NATO, is largely westernization, and modernization, which is needed in order for a global union to be established, in addition to its defensive tactics. NATO is meant not solely for defensive purposes, by also rippling through the military by improving its economics by making more and better weapons available through its use of better and more useful development of weaponry.
Yes, NATO expansion benefits European politics and integration, because allowing more counties to participate is always a positive thing. With strong traditions, NATO can involve other nations and still fulfill its purpose. Allowing more nations to participate improves the conversation between countries, and leads to increased stability and an improved economy for everyone. Expansion is positive because it improves discourse, stability, and the economy for all nations involved.
NATO is for defensive purposes and military alliances, not for political gains. Expanding NATO does nothing for integration of Europe's politics or integration of new countries into the European Union. NATO should be replaced by the EU's combined military when the country expands. Once Europe becomes more unified politically, a common defense can be realized.