Eble. If the idea was really pushed in the back-rooms as a way of allowing countries which don't speak the official UN languages to participate more fully, then such countries might vote in favor of the resolution even if the larger countries vote against. There was a significant amount of support for Esperanto in many countries, in Eastern Europe for example, and smaller countries might have been convinced, as I said, by lobbying.
What is the extent of the resolution, though? It might have even been possible to add Esperanto to the official UN languages, requiring real-time translation and translation of documents. I don't think an actual mandate to teach Esperanto in schools (and to adults) would be possible, although the use of the language at the UN would encourage people to learn it.
Esperanto is, of course, not a difficult language to learn and it's a very easy language to translate into. (My problem with it is that I already know three of the source languages to a fair extent -- English, French and German -- and I have to guess which of those languages the Esperanto word comes from.) At the opposite end of the spectrum, the UN could simply encourage the use of Esperanto to a greater extent than it did OTL (UNESCO did, in OTL, endorse it to some extent).
I'm not sure how likely adding Esperanto to the list of official languages would be, but it would be, in general, a good thing for the world.