Would having a number of collision components result in huge performance hit?

I’m working on tile based strategy game right now and I wanna add height map.
To achieve this I’m thinking about adding a collision box to each tile(tiles that are supposed to represent mountain, slope, etc).
At first the idea seemed simple and good enough to go with, until my colleague pointed out having thousands of box collisions in the level would significantly decrease the performance.
Although I disagree with him, he did bring up the valid point.

Hence my big question; Does having thousands of box collisions affect performance(on mobile) a lot?