This is just my opinion but here goes.
Do you notice a difference in falsing between having the cover on or off ? That would be one simple answer to your question.
My experience with the AT Pro in salt water is that I don't think that falsing it's related to the coil cover at all but rather the difference in conductivity.
It think what you are experiencing is quite normal for the AT Pro used in salt water and turning down the sensitivity a couple bars is also not unusual.
For salt water... First ground balance it in the salt water, you may even have to make manual ground balance adjustments to quiet it down (falsing that is). In New England salt water My AT Pro seems to like to work best when balanced somewhere between 13-20 (in salt water) and the sensitivity down a notch or 2 from where I use it on land. In Salt Water I tend to keep the sensitivity set to the point where the detector chatters a little but is a pretty uniform chatter for the most part.(almost like background noise). That's no big deal and when you pass over an actual target you will definitely hear the difference. I've also had times when it runs pretty darned quiet in salt water.
You need to re-balance if you leave and go back to the dry sand. On land, or in dry salted sand my AT Pro balances quite well automatically, usually between about 87-93 and falsing is rarely a problem.
Check out this Garrett "tips" video with Steve Moore ... it's right on the money!
Using the AT Pro - Salt Water Tips
As for the coil covers. I'd say keep it on. But...there are also lot's of folks that don't use them at all. I believe they can save you from damaging/chipping the $$ coil when you happen to swing into a rock (and you will). You could always take the coil cover off and clean it if you're concerned about sand and salt collection in there.
This brings be to a pet peeve. I feel that those Garrett coil covers really lack uniformity and sometimes don't fit at all, or fit sloppy. They are also very thin and flimsy and can easily split when removing them and re-attaching them. I've dealt with that problem by attaching all my coil covers with Silicone glue. The covers then never come off, never leak, and never collect dirt and grit. It's a pretty messy job putting them on neatly with silicone glue but to me, worth the effort. If I ever wear out, or crack a cover they are still pretty easy to remove and replace without damaging the coil. Covers have been on my ACE 250 coils for about 8 or 9 years. I've never had a cover problem and they still look almost as good as new.
