From what I understand, if you plan on leaving in less than 3 weeks, they won't do PR renewal urgent processing, and will tell you to apply for PRTD from the country you're traveling to. Nobody could tell me how long PRTD takes, it probably depends on the country. I saw someone on this forum stuck somewhere in europe for 3 months with no updates to their PRTD application, so that is not very convenient if you need to return to Canada in less than a few months.
Though it probably won't hurt to call and ask if it is possible to hurry it up.