Can I install with a populated MySQL database

If I install contao-2.11.3 using an already populated MySQL database will contao delete any tables in that database either during installation or afterwards?
Is there a list of cantao table names that only it will use within an already populated database such that if none of the tables already there are named the same as any of those, then the tables already existing will be safe?

I think as a general rule, all of Contao's tables are prefixed "tl_". Some extensions may use tables without the prefix, but Contao won't modify them unless told to do so.

It's just the tables with this prefix that Contao tries to auto-manage. It does so by searching all of the module config folders for "database.sql" files, and compiles them together to build a single SQL statement for each table, and checks for missing/orphaned fields and tables, and updates accordingly.

So long story short, as long as your existing tables don't have this prefix, you should be safe.

And if there are any conflicts, you can add your own "database.sql" file into /system/modules/{any folder}/config/ with your table's configuration (you can take a look at the existing ones to see how they're setup).