Simply : Not a good idea!
The issue of taking care of old and ill parents is a really important one and since the government isn't making it easy for people like you to bring their parents to Canada and take care of them over here, than I guess your choices are limited. However, expect your application to get an RQ and so on... the rules for today are still the following :
1 - no criminal offence
2 - 1095 days of physical residency in Canada as a PR
If you fulfill these rules and have no choice but leaving after applying, just make sure to have a place to receive your mail in Canada.
Again : It is really not recommended to leave after applying... once you will become canadian, you will be free to do whatever you want.