While TSA states that it can take as long as 72 hours from entry to processing and an OK for Pre-Check, that is almost always way over the top.
I have booked tickets for last minute business trips while on the way to the airport and arrived to have the ticket pushed and received Pre-Check.
The issue is not how long it takes TK to process the number, that is reatively close to instant, but whether its interface with TSA is instant.
The vast majority of the time, you should be able to enter your KTN, print a BP and have Pre-Check within the space of the time it takes to get this done.
The TSA website incidentally, maintains an updated list of carriers participating in Pre-Check. TK is on it and the list expands regularly.