Joseph:
From a legal perspective, the 1947 UN Partition Plan was irrelevant – it was a General Assembly resolution, which means it was only a recommendation, and it was rejected by the Arabs, which means it never went into effect.
From a political perspective, the UN’s approval of the Plan certainly helped Israel’s international standing.
Whether or not the individual countries would have recognized Israel without UN support is, of course, impossible to know, as many other factors would have come into play. The important thing to remember, though, is that Israel doesn’t draw its legitimacy from the UN, and its rights aren’t limited to those granted by the Plan.