Brokeplex, in the film and in the short story, I believe Lureen says something to the effect of "half his ashes was interred here, and the rest I sent up to his folks". Why would we question her using the word "interred", which according to Webster means, 'to put into a grave; bury'. What's your premise/theory for us not believing her?
By the way, I voted No, and I agree very much with Chrissie as to why. Lureen would have been mortified beyond belief is those ashes had to be dug up, and some explaining had to be done. I think if Lureen had actually ever met Ennis or spoken to him on the phone, even, before Jack's death, that things might have been different, and she might have been a bit more sympathetic to Ennis's grief. But that wasn't the case.
I also voted No because Ennis was never a man who needed many material objects in order to survive and live his life (or the semblance of the life that he led, more correctly). Why would he need an urn of ashes to remind him every minute of every day for the rest of that life, of Jack?