Battery is lead mostly, no iron, so I suspect not, but test. Normally we think of non ferrous metals as non magnetic meaning lead is non magnetic.
However the flowing charging current and voltage to the thruster battery will create a magnetic field around the conductors and in the battery itself. Maybe that is strong enough to upset the compasses ability to sense the earth's field and thus give a good signal to the A.P.
This effect would most likely be strong on one heading and weaker at 90o so should also affect the compass more or less depending upon heading unless the wiring and battery partly surround the compass.
Try disconnecting the battery, ensuring that the leads are well spearated and cannot get into anything, and test. Pull the fuse.
If the problem quits and the A.P. works again then you have your answer.
If not then try removing the battery and retest.
If either test works then you must decide whether to move the battery and conductors or the compass.
If the above works There is one other possibility and that is twisting the positive and negative battery leads around one another. This will cancel out the fields around the conductors. You may have to lengthen the leads to do it so try just killing the power first. Maybe that will be enough.
If neither helps then the A.P. or compass likely has another problem coincidental with the battery install. Did you monkey with, damage or disturb the compass wiring in ANY way while installing the battery? These leads can be somewhat fragile.
Yes, I'm reaching here but have seen my own compass foobarred years ago by a knowledgeable??? installer installing a small speaker close to my compass. Compaii do not like that.