Sorry, I don't understand the question of a "seasonal overlay". Do you mean like the HM in DL during Christmas? Are you thinking making changes to the ride for a couple of months out of each year to strip out Sparrow? If that's what you mean, I don't understand why they'd do that. That's a complete revamp of the ride, both animatronics and tons of audio throughout. They won't make a temporary change-over frequently to strip him out for short periods of time.
As to the question of PotC with or w/o Jack in general, I'm a big fan of the first three movies. I'm a big fan of the character. That said, I'd be okay without him in the ride. Like @Walt Disney1955
said, I don't think the tone of the ride changed so drastically with his addition. Maybe his placement at the end of the ride is a little too prominent, but I understand why they did it. It seemed appropriate given the popularity of the movies. Besides, the end of the ride in MK was kinda blah before his addition. Adding him at the end gave a better end to the ride, but they probably could do even better without him if they really wanted to.
They might take him out eventually, but I don't see that happening for a long time. That would cost money that Dis doesn't want to spend.