Someone suggested that with the Alpha 3000 (this was something I vaguely remember from somewhere)...
If you disconnect the fluxgate compass (there are connection on the compass that should allow you to do that) -- then turn the wheel and turn-on the compass.

If the wheel doesn't center, then it's probably the compass that is causing the issue; and, if it doesn't, then it's either the board on the compass.

I DON'T KNOW IF THIS IS CORRECT, you might call Alpha and discuss it with them.

It is possible that the Alpha has some issue with the ground causing a backfeed. I have heard of boats that have a variety of issues when the broadcast while using the autopilot... As for permanent damage, I guess it's possible, but I'd suggest that it would be wiring issue rather than the pilot because there are bunch of Alpha out there that are long-range cruisers.

When you broadcast, have you had some other DC items on and noticed anything? Have you tried to hook-up a digital meter to i) your positive and neutral of the wires connected to the autopilot. Thry keying the unit and seeing if you see anything unusual. Then try and check to see if you're getting any current across the neutral and a "GOOD" ground while keying it.

After having said that, things do coincidentally happen. BUT BEFORE YOU GO BUYIN A NEW PILOT -- i) talk with Alpha and ii) Check around a bit more.