There is nothing barring you from doing this, but have you looked at the RQ? It's not something to fill out on the fly. You would have to have it filled out well in advance and have all the documents. There are more than a few.
The question is: Why do you want to do this? Why do you want to borrow tomorrow's problems for today? A problem that, statistically, you are unlikely to face. Why do you assume you will require an RQ? Is this assumption well founded and well-researched or is it based on uninformed fear?
Many people try to outsmart the CIC and outgame the wait times, but in my view such attempts usually help little and sometimes cause harm. Harm in wasted time, undermined credibility and unnecessary stress.
Torontonians please note: Toronto-area RQs are processed at St-Clair, but Yellowknife, Iqaluit, Vancouver and Fogo Island RQs certainly are not. I got an RQ in Montreal and it was processed in Montreal.