Can one make any guesses how a player will play in the Major leagues based on his performance at the AAA level? If he is a AAA all-star, can one surmise that he will be able to be a decent Major league player?

Not at all

Minor league performance has almost nothing to do with major league readiness. Just ratings.

Many teams don't field an honest roster with 100% healthy pitchers and position players that belong at that level in the first place, so stats are not a great indicator. Ratings are the input

I'm weary of guys who struggle at the MiLB level, especially pitchers, but don't put any stock in the stats of guys that succeed.

That is what I thought, but one of my first rounders was being outperformed by someone who may or may not make the big leagues. I will chalk it up as an anomaly.

The biggest difference I notice in AAA vs the majors is splits vs power.
In AAA you can have a guy with 91 power, contact in the 50's with splits in the 30's that can hit 50-60 homeruns.

In the majors, even with 600 at bats, that same player will probably hit 20-25 homeruns but will strikeout 150 times. and have an on base below .300.

Three things:

1/ I've had players - mostly the pitchers - who put up average minor league stats, but their ratings made them good major league pitchers just the same.

2/ Similarly to the example hockey1984 gives above, I've had AAA SPs who pile up wins because they have great DUR/STA, and splits which would never get them to the majors. Those SPs win Cy Youngs in the minors.

3/ The necessary jump in talent level / ratings between AAA and the majors is probably greater than between AAA and HiA/LoA.

Keep in mind that you don't choose your minor league parks. All of them may be wildly different than your BL park.