Yes, that will fix the problem.
The alarm module has 2 small batteries of its own.
If you have changed the alarm and open it upby using a saw, it probably lookjs like this.

To get to the alarm module, you have to take of the windscreen wipers, than the black cover.
When doing that anyways, also clean the small waterhoses that take down rain water from that area and take out all leafs and other debris.

Good luck

Alwin