Nope... they will check the date stamps in your passports. So to be on the safe side, include all the dates that you spent here separately in sri lanka pcc. You can take a pcc for the complete period in qatar.. in this way it will look more genuine
Yes they will check the date stamps on the pp. Also, when you fill out the EE profile travel history they will ask your resident location at the time of travel. I.e I lived in the Bahamas from October 2012 to August 2016. During this time I'm a Bahamas resident, Sri Lankan citizen. So, I should obtain a PCC from Bahamas police for that period. While I was a resident in Bahamas I have done various travels to US, CUBA other Caribbean island and as well as SL for over a month for vacations. Those are my travels. Technically those are not my residencies during 2012 to 2016. There is an exception if you have stayed more than 6 months in one place as per IRCC regulations.
So as you suggested when you fill out the address in SL you will have to fill out SL address every time when you travel to SL for even two weeks per year. The ultimate outcome is your SLPCC will get delayed while you are trying to be extra smart.
If you go by the law, in my scenario my permanent resident address during 2012 to 2016 was Bahamian address and I should not be issed a SLPCC for that time.
This is my experience and knowledge. Anyone can have different opinions.