If Iraqis were given these tanks, they probably were given some maintenance facilities to do this overhaul. Otherwise they'd have to send lots of heavy engines to the USA. That requires lots of spare engines in the loop, as the service turnaround can be measured in months. I think a few rebuilding workshops are much cheaper than hundreds of engines.
Besides, the distance from Ramadi to Baghdad is only 65 miles - just an hour or two of running those tanks. The Iraqi army is running out of space to retreat to.
It may also be that those 700 to 1,400 hours are prescribed on basis of guaranteed reliability and then serviceability. However ISIS can run those tanks until the engines die and cannot be rebuilt anymore. That could be as much as 5,000 hours, perhaps (I don't know.) Weapons are expendable if necessary - especially those that were obtained for free.
Surely they would stand and fight for Baghdad. But, I dunno - the Iraqi "Army" sure hasn't impressed.