Unthinkable for TPE certainly. Plenty of other operators have brought in old emergency stock to reduce overcrowding.
Yes unthinkable is perhaps a little strong but how about very difficult? That seems fair. HT managed it mostly because they were staring down the barrel of just not being able to a run their service full stop (yes TPE have had some terrible days but nothing like HT had in percentage terms at times before the HST!). Other operators manage it on an ad-hoc basis such as XC during industrial cobbled together a charter operator to provide a service between York and Chesterfield for instance or Northern to provide a service on the Windermere branch. But those were exactly that ad-hoc. The only other places that have done it long term have been Greater Anglia and Scotrail and there the rakes were in use for years (or still are!) so going through the rigmarole of organising crew training, clearances, insurance cover for a different style of operation, depots for the temporary stock, etc etc. Then remember that this gets in the way of training crew on the new stock and preparing for their introduction behind the scenes so could very well delay the new fleet even further.
Impossible? No, of course not. But difficult? Very. Potentially furthering the disruption? Yes, quite possibly.