Could engine damage occur while waiting on replacement transmission

[Kiwied]

My 24 XLT was diagnosed as needing a new transmission at 9230 miles. Local dealer service department gave me the truck back and ordered a new transmission from Ford. It is my only vehicle so I have been driving it to get the kids to school, to work, while the transmission issues are getting worst, including engine rpm sticking at high rpm when I take my foot off the accelerator..does anyone with experience know if the engine can be damaged by the faulty transmission Ford put in my truck?
Service department have the new transmission now but no courtesy vehicles, which they say, could take some time to make happen?
Because I ordered the truck through Ford could they possibly be responsible for a courtesy vehicle through a local dealer while their faulty transmission is being changed?

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[Hootbro]

Unless there is some slamming shock loading on the engine to cause it to go to redline, should not really be an issue in the short term. Still not ideal though IMHO.

As to a courtesy vehicle, as the name implies, it is a courtesy and not an entitlement you get one while down for service.