I'm sure it does .....but have you tested it to see if it is working correctly? Have you load tested the battery?
I believe your rectifier is built into the MPEM, I have a 98 GTX LTD, and mine is built into the MPEM...its a bummer but I have seen an attachment that will correct a bad rectifier for our MPEM, if that is you issue. Not saying it works, I haven't tried it.
Here is the simple test to see if rectifier is working. Crank up ski, put multimeter on battery terminals, read voltage, should be in the 12V range. Rev motor to 4500 rpm, watch meter , it should go into the mid 13V range to low 14v range. If you get a reading lower than in the 12V range at idle then it is bad, if you go past around 14.3V(ish) when at 4500rpm it is bad. If you don't get into the 13V range at 4500 then it is bad. (you want mid to high 13V range)
Do all this quickly, you don't want to run the ski out of water for too long. Whatever you do don't jump the battery with a car or power pack, it can ruin the electronics.
Let us know how that goes and we can see what else could be the issue.