Which specific integration are you using? Hopefully the one based off of the ST Harmony Hub integration? That's one I believe most of us are currently using.
Assuming that is the correct integration... Yes, you should expect a delay of up to about 5 minutes... Not ideal, for sure...
I haven't noticed this. But truth be told, I probably would not notice it as I use the integration to simply start an activity as part of a larger routine/scene. I do not use the status of the Harmony Activity 'Switches' for anything currently. I'll try to test it later and report back my findings.