1.
Its not possible to prevent the Exchange Server content indexing during work hours (the only workaround would be to start/stop the indexer service). However if you disable the service, your users will get an error message in Outlook clients when they perform a search. I also wouldn´t try to disable the index for a DB inside a DAG (see here if needed). Because if the index is not working correctly (e.g. service isn´t up and running or the index is disabled on a DB) an automatically failover in your DAG will not work (see here) and you need to move mailboxes by hand via:
Move-ActiveMailboxDatabase <database> -SkipClientExperienceChecks -ActivateOnServer MAIL1
if something working as expected. You might also reset the index fully if it becomes stale (see here) which then takes much more time then having it up and running.
2.
However you can fine tune the indexer. For example if the default 32MB attachment size is to big for your environment (e.g. due to the reason that most users work with Outlook in cache mode which use the local PC index) you can limit the Server index to 2MB. You can also disable the indexing from some file types like ZIP files if needed. I think that fine tuning the index might be the much better option in your environment as disabling the index will kill most DAG features. As the fine tuning from the index might be off topic for your question I will not go into details here. You can find various options here for example. I also would reset the index fully after you did some fine tuning here so that the index only contains the fixes which should be indexed and no old one.
Advise: If your Exchange server is over the capacity, I would start to use the Office Cache mode, prevent using OWA and fine tune the index process and build and assign a own Client Throttling policy. If this isn´t possible or didn´t help you need more CPU power.
