Expansion // Explosion and Alms Collector
Yes, Alms Collector will replace Explosion's draw effect, for the reason you mentioned.

The exact order of events is like this:


Explosion starts resolving.
Explosion deals 4 damage to Alms Collector.
Your opponent would draw 4 cards as the result of Explosion's second instruction, but Alms Collector replaces that effect. Instead, you and your opponent each draw 1 card.
Explosion finishes resolving and goes to the graveyard.
State-based actions are checked. Alms Collector dies because it has lethal damage marked on it.
The active player gains priority.