Well Andrew refers to 3-3.5 half squat or higher than parallel, jump specific squat, not a full squat.
But yeah, I agree that you need/can train neurally a lot. The question is - are you going to improve as much and as quick, in terms of relative strength, as a guy who also gains a little muscle?
You could also go and build a little muscle and increase your squat quickly and then cut down on the calories and start losing weight, maybe fat maybe muscle, but now you're going to have a weight that you can use in your squat (a newly established, higher squat 1RM and 5RM) that you can use while cutting down on weight.
So you can be:
180 lbs with a squat of 250
GO TO
190 lbs with a squat of 300
then cut down back to 180 while using the same work reps and trying to maintain that 300 squat and end up being
180 lbs again with a squat of 300
I think that can make your CNS adapt quicker to the load, muscles as well etc, but it's going to take a good planning in terms of training and nutrition to make that happen I suppose. Your body will probably be more inclined to accept that weight as "managable" and will happen quicker than if you were just to stay at 180 and try to improve to 300 on your squat just by neural adaptations alone.
i don't recall seeing people successfully do that on forums etc.. most people gain weight then have major issues taking it off while maintaining strength.. as easy as that sounds, it's actually harder for people to gain weight + gain strength then cut that excess fat while maintaining, most everyone seems to have major issues doing so.
i could gain 6+ lb in one day if i carb'd up, so, gaining weight indicates much more than just 10 lb to me, most of us could put on 6 lb in one day just carbing up with glycogen/water retention, that's nothing special..
to me it's easier to stay around your goal weight and work from there.. if you have no goal weight then fine, but if you do, like myself, no point ballooning up as it just becomes too hard to cut back down while maintaining strength due to the intensity/stress of my training.
i'd rather stay at 150 and improve from here, eating too much actually hinders my strength gains as i become even more lethargic, fat, and ogre-like.