H-E-DOUBLE-HOCKEY-STICKS NO!!

Myself, I would not. That's a fair bit of money to put into a vehicle that isn't going to bring a whole lot if and when you want to sell it.

I did a bit of noodling around Edmunds, and it looks like most Sorentos in your vehicle's general age and mileage range are going for about $4-5K, with a few examples asking closer to $7000 to $8000.  And that is dealer resale price. 

The other issue is what else is going to need work in the future?   You've done a good job taking care of the vehicle to get 230k out of it.  As someone who has owned several Hyundai's, I'm impressed.  But I think there's a legitimate question to ask how much life the vehicle has left in it at this point.

The only pro to having it fixed, IMHO, is if financial circumstances preclude getting something else right now.  Cars are freakin' expensive in the current economic environment, even used ones.  And sometimes you've got to make the best of what you have on hand.   If there are other options, though, I wouldn't take this route.

v4

no such thing.

2.4

GDI or MPi?

If it's the MPi G4KE then it's a reasonable engine, issues usually are caused by a catalyst felling apart and chips ruining the cylinder walls - to determine if your car has scuffed cylinder walls there's no reason to save it.

Generally the 6AT suffers failures due to valve body contamination, and it has a large and expensive one - I would recommend attempting to find an inexpensive used replacment from a junkyard, just make sure it has a warranty.

But y'know it's a 12 year old car with lots of miles on it, don't put too much money into it.