You get to draw a card from Alms Collector's ability in any case.
You are correct that Narset's passive ability is not a replacement effect, because of 614.17, but that has no relevance here - 121.2a solely exists to enable the Alms Collector replacement effect.
121.2a An instruction to draw multiple cards can be modified by replacement effects that refer to the number of cards drawn. This modification occurs before considering any of the individual card draws. See rule 616.1g.
So what happens is that Alms Collector replaces the multiple card draw event before Narset is even considered because of the second clause in 121.2a. You and your opponent now each draw 1 card. If your opponent already drew their card for the turn, Narset will prevent their Alms Collector card draw, but you will get to draw your Alms Collector card in any case.
609.3. If an effect attempts to do something impossible, it does only as much as possible.