I was in the same situation, and your question is absolutely legit. Hope my reply helps.I recently started gathering materials for my PR application via express entry under federal skilled worker program but now I realize that this might take 6-9 months. As I would like to work in Canada already at an earlier time as a data scientist, I am considering applying for a temporary work visa to start ASAP.
Can I thus immigrate on the temporary visa and switch over to the PR once the express entry got approved? Or is PR express entry only available to those who remain outside Canada for the entire duration of the express entry application process?
I had a visitors visa to Canada before applying for PR. After applying for PR thru' Express entry from outside of canada, I entered canada on visitors visa. My category for PR was FSW-outland.
Based on my experience and talking to multiple IRCC agents thoroughly this is how the process works.
If you are in canada with legal status (visitor) and your PR application is being processed you can apply for 'open work permit'. For the application you have to specifically send (online) it to the VFS/VAC in your country (or the country from where you applied to PR from). If you send the online application to any IRCC office inside canada it will be automatically rejected. If you are qualified you will get approved in 2 months on avg. You can start working immediately and the work permit becomes invalid if you get your PR before its expiry.
In your case I understand you dont yet have Visitors visa. In that case I will suggest you to apply for visitor visa even before applying to PR as it barely takes a month. then apply for PR --> then enter canada on visitors --> apply for work permit.
Also I suggest you to call IRCC and verify this process based on your situation.