We forgot the most important parameter. The frequency "jump". If the frequency change is large, i.e. from 10 Khz to 1 Ghz, then of course it will take longer for the tuner to equilibrate. In my scanner, when I approach a target I take 10 baby steps of 2 Khz each to zero in. Drift is negligible. I tried using the 5000 us in my scanner, and the results were the same as without it, except for the delay of an additional 50 s. I promptly removed it.
The way I see it, tuner needs some time to settle in a new frequency, but there is no fixed delay. It is situation specific and depends highly on the amount of frequency change.
HTH,
Nikos