Can 100 push-ups a day help your arms to get significantly bigger?

Significantly, no, slightly, yes.

That is because your body will get used to them over time and they will become easier and easier to do. If you add a bit of resistance and variety to them, there might be bigger changes.

If you want to squeeze all the results out of push-ups on a daily basis, mix things up.

For example:

Monday: 100 regular push-ups

Tuesday: 100 decline push ups

Wednesday: 100 diamond push-ups

Thursday: Rest

Friday: 100 weighted regular push-ups

Saturday: 100 wide push ups

Sunday: 100 chair dips/parallel bar dips