Shouldn't be allowed. The issue is that even though Drogba is recognizable, the Ref keeps track of players via jersey number - that's why it's in the rule book, same as offsides, handball, etc. What happens if a second player rips their jersey and they don a numberless shirt? Answering that the second player can't step on isn't valid - neither would be playing with the number assigned to them on the starting card, so neither should be allowed on the field.
MLS dropped the ball here by not ruling him ineligible. It'd have been a tough pill to swallow for Montreal by forcing them to burn a sub, but it comes down to Montreal's equipment manager not being prepared - same as if he bring three types of cleats for each player - be prepared for anything.