I know that in a normal atom the Heisenberg uncertainty principle prevents the electron from doing this, but what if there was an infinite attraction (infinite force) between the nucleus and the electron? Would the electron fall in then?

Once you set up a physically impossible scenario, you can get pretty much whichever answer you like, since there is no physics that you can validly apply. You can't have an infinite force, so the scenario is moot.

However, you can look at the scenario without putting an unreasonable constraint on it, and the answer is yes, if it's energetically allowed. Electron capture is a known decay mode of nuclei with an excess of protons. For the proton and electron to combine, the formation of the neutron and neutrino must release energy in order for this to happen spontaneously. As a bare neutron is more massive than a proton, that only happens when the N/Z ratio is low compared to that of stable nuclei of similar mass.

One could extrapolate this and see if it becomes more favorable if the electrostatic interaction were stronger, with all else being the same*. That would imply that protons in the potential well had a larger repulsion, making it more likely that converting to a neutron would release energy.

* in reality, this would likely have other effects as well. 

This also happens (or is predicted to) in neutron stars where the extreme gravity overcomes the electron degeneracy pressure.

Ok, so there is a finite pressure where electrons collapse into the nucleus? 

3 minutes ago, Hami Hashmi said:

Ok, so there is a finite pressure where electrons collapse into the nucleus? 

Yes: https://en.wikipedia.org/wiki/Electron_degeneracy_pressure

https://en.wikipedia.org/wiki/Neutron_star