Oh yes they will. if the warranty company can locate a less mileage motor pulled from a junker, they will most certainly try to use it. Fortunately for us, the HO 3.5 isn’t as voluminous, so easy to find the standard 3.5TT, not as easy to locate a low miles used one. If that doesn’t work they go to an aftermarket remanufacture like Jasper.
But all that assumes you have the stomach to fight a 3rd party warranty provider, like say... someone you would be in better than average hands with or some company that might have animals prominently featured in their commercials, or fer’n accents used to pitch the service. These companies have a threshold of cost which they will allow for uncontested repairs, and it’s typically pretty low. Anything above that threshold is held pending denial. They then slow walk their “adjuster” out to evaluate the vehicle and failure. He reports back on the problem who then “evaluate” the claim which can take a day, a few weeks or a month depending on how much they want to fight you. Then they deny it if there’s any grounds - you missed a receipt indicating you may have not checked the brakes at one service interval, never mind that has nothing to do with the motor failure... You get to argue with their level 2 adjusters next, who will work with you, “out of the kindness of their hearts, even though your case should be denied”. Then they offer to pay a token amount, out of “customer goodwill”. When you’re done with this crew, the next team are more serious about negotiating. It helps to have a lawyer call for you at this stage. Some companies offer legal plans that cover all manner of things, like insurance issues. This makes life a little enjoyable actually. Have the lawyer conference you in for a fun listen.
During this call, the lawyer will likely set a firm deadline for a response, with the promise of legal action for breach of contract if the deadline is missed.
I know others on here have had some positive experiences. Good for them and I’m glad they did. I’ve not had that experience and those personally known to me who have also gone the aftermarket warranty route, all of them, had similar stories for expensive repairs. YMMV.
And think about this, the mechanic isn’t working on only your car/truck, he’s got other things going on to pay the bills. if your drama starts sucking up his time, and not making him any money, how motivated do you think he’ll be to walk your warranty adjuster through the problem for a 2nd or 3rd time?