Personally, I very much doubt it. I'm not a physicist, but a compass needle is simply a magnet that is freely suspended (in two dimensions). It will point to the strongest magnetic field in the vicinity. If anything, this should strengthen the compass, not weaken it.
One possible exception would be if the compass needle were placed perpendicular to a strong magnetic field for a long period of time.
I did a google search on 'degaussing' and 'compass' and came up with this web site, which (among other things) describes how to degauss an object that has become magnetized:
http://www.sacskyranch.com/degaussi.htm---------------------------------------
How does it demagnetize?
Alternating current from the power supply sets up a magnetic field in the degausser that reverses itself sixty times a second. This causes a magnetic field in the object you are trying to demagnetize that also reverses sixty times a second.
To reverse the magnetic field, the field must pass through a point of zero magnetism sixty times a second. Now the magnetic domains don't like changing direction so fast so they act differently during the positive cycle than during the negative cycle; this is called hysteresis.
By decaying the field the hysteresis curve becomes smaller and smaller (less magnetism). Eventually, the magnetic domains orientation becomes random. The magnetic fields are always present in any object. It's just that you mixed up all the magnetic domains so that they have random directions and all their little fields cancel.
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I have no idea offhand whether this person is talking through his hat or not. (But I do know of cases where VHS tapes were degaussed by people leaving them on top of the VCR while other movies were playing. I'm pretty sure the alternating current/fluctuating magnetic fields generated by the VCR were the key to this. And AFAIK, it only happens to tapes that are left there for extended periods.)
If you want to carry a compass and a magnetized tool in the same pocket, I think an alternative solution would be to clip the two of them together, so that the compass needle is semi-permanently lined up with the magnetic field. If this isn't an option, then I suppose it would be better off separating them. But I think the chance of your compass being destroyed in this fashion is very low.