As noted on both https://www.edmunds.com/car-maintenance/how-to-prep-your-car-for-long-term-storage.html and https://www.dmv.org/how-to-guides/storage.php they seem to suggest that leaving old oil in the car can corrode or damage the engine. Given a car that has oil that is halfway between oil changes (let's say 30k miles or 2 yrs, whichever comes first), does letting a car sit in storage for 2 months with older oil cause more damage than running it regularly for 2 months with that same oil?
There's two parts to your question which I'll touch on.
First, oil which has been run in a car for any length of time will have condensates in it, which when mixed with the oil and it's chemicals, can create acid. This can, over a long period of time, cause issues with the soft parts of the engine (mainly bearings and seals). An engine which is run regularly should not have this issue because most of the condensates will evaporate during each engine cycle. They aren't in the oil long enough to cause any major issues.
Second, I would not consider two months to be long term storage. For this amount of time, I'd fill up the gas tank, make sure the tires are up to pressure, and disconnect the battery once parked (or alternatively, put a Battery Tender on it). If you are going to leave it sitting for six months or longer, then I'd consider it long term storage (this is my guesstimate, so take it for what it's worth). I'd not consider two months to be any issue for the oil, and definitely for the other parts of the car given you do as I suggested with fuel, tires, and battery.