If you already have a boarding pass for your flight out of HKG there is no need to visit any check-in desk.

The only reason to visit a check-in desk would be if you have luggage to check in. Normally, your bags should be checked through to your final destination so you would not need to retrieve them when you arrive in HKG, and thus you wouldn't need to check them in again. But if there is something you need in your checked bags while in Hong Kong, then you could ask for them to only be checked to HKG, and then obviously you would need to recheck them for your second flight.

Immigration shouldn't be an issue.