Is it possible to have the built in reports query a replica of the database? If so, how?

You can export the whole database of an installation, you have a button for that in the configuration menu.
Then it's up to you to build the queries.

What I'm trying to achieve is to have the reports run from a mysql replication slave instead of the main DB.

ok: you're trying to generate the statistics from the LimeSurvey Admin Interface, but using another DB. Correct?

That is correct.

well... If you copy the whole LimeSurvey database, you can just change the DB settings in the config file. It will work.

So there is a separate DB settings configuration just for the statistics section of the platform? If so, where can I find it?

No: there is not.
I'm telling you that if you copy the whole DB, then you can connect LS to that DB.
But it will affect the whole application, not only the stats.

OK. So I guess the solution here would be a separate LS instance configured to use the read replica, which is read-only, for the reports as making changes affecting the entire application is not acceptable. How can I disallow the use of statistics? I would like to prevent people from running statistics on the main DB.

also, maybe this will interest you:
www.reportico.org/site/index.php

and:
github.com/reportico-web/limesurvey-reportico

Reportico looks nice but I'm not interested in designing new reports, at least not at the moment. Sometimes my users like to generate reports for fairly large time periods and have found that they can have a significant impact on the database used by users when they are filling surveys. I want to avoid that by not allowing reports to be run on the main installation/DB. Correct me if I'm wrong but, commenting lines 500 and 501 on admin/admin.php would effectively block the functionality, right? I realize it may not be the most elegant way of achieving this. Alternate ideas for achieving what I have described are welcome.

which version of LimeSurvey are you using?