It depends on the boat and the installation of the generator. The bigger the boat the more likely it will be fine. Smaller cats can easily get the water pickup out of the water coming off waves when sailing fast. It was a problem on my Voyage 440. It’s not a issue on the Leopard 50. Having said that if you want to have nice cool air at night sleeping and minimize generator issues start it in the evening and shut it down in the morning. No need to run it during the day. You increase your chances of something going wrong, impeller failure, sucking in debris ect… The generators also typically require a 100 hour oil change and if you run it all the time you will exceed that early on day 5.
On the restriction given to the OP for run time it’s not normal. There is no point in having the Genset at all if you are going to do that. You are essentially chartering a boat without AC and that should come with a very large discount. It’s possible the generator is not sized to run the AC in which case the boat should be advertised as dockside air only.

Edit: Checked the Genset manual for my boat and only the first oil change is 100 hours. It’s 250 after that.