Does testcomplete have a code indexing feature?

The built-in Ctrl+F can search the entire project suite and supports wildcards and regular expressions, just FYI.

Or you can use the search functionality of your operating system or source control system.

Not an indexer necessarily.  There is the "code explorer".  In the default docking of TestComplete, it's one of the bottom tabs in the left side.

This lists out all the units and the functions within those units on a per project basis within your project suite.  Other than that, the best way to find something specific in your code base is your standard ALT-F Find function.