Pretty sure "cores go bad" on just about anything (depending on a lot of variables). Besides "W123", you don't mention "year, model, mileage, condition, etc". That info would influence which direction I would go, for sure. Also, possibly, how much other money I was gonna sink into the car. Is your car a "mint condition, low miles cream puff or a rusted out, high mileage beater"? More than likely, somewhere in between.
Changing the core in a 123 can be a daunting task (as would a core change in any MB ever made, I'm assuming). If MB has a major fault in their outstanding engineering, across all years and models, it would be the placement of evaporator and heater cores IMHO.
I'm probably gonna get crucified for this next statement, but, I'd put some "stop leak" in and see what develops (or doesn't).
I'm of the opinion that if your heater core is already leaking, and in a somewhat compromised condition, an aggressive flush treatment might make matters worse.
Fill 'er up with the proper mix, add some stop leak and drive it for a while. You may be pleasantly surprised (or not).
You could also drop the fan under the dash (easy job) and using an inspection mirror see how much fluid might be in there (and also gently flush that area with water, in the process). Make sure the "drain tube" is open and functioning.
You can always go all Rambo on a bunch of "balls to the wall" flush and fills at a later date if you feel it's prudent. If it were me, I'd "tread lightly".
Just one person's opinion......