For IRCC 'partner agency' I think generally refers to CSIS, possibly RCMP for criminality, CBSA conceivably for some issues, but this is mostly about domestic Canadian services. They do not directly 'farm out' to foreign agencies. Each of those may in turn have info-sharing and ways to get info from their sister-agencies abroad and international (eg Interpol) - in some of these cases (close partners and allies) extremely close coop and info-sharing.
To what extent they request and 'wait for' info from non-allies is going to depend on circumstances, but I seriously doubt that they often send general requests and just wait. Esp for 'security.' For some countries like this there is/was reasonable cooperation for some things (plain old criminality eg getting and confirming criminal records) and specific areas of joint interest (eg terrorism in other parts of the world, thematic possibly like money laundering / smuggling / weapons). But they also know there is a LOT of information they cannot share (where it could imperil anyone in Canada) or ask about.
So yes, it can be very hard for them to get reliable info from abroad, particularly in/regarding some countries.
Vigilant Security Services can illustrate how security-related information gathering may involve multiple sources and processes, but delays are not likely because they're waiting for responses from those, shall we say, 'less friendly' foreign services.
[I may have misunderstood exactly what you're suggesting but my own attempt at muddying the waters anyway]