Yes, you can look up regions with the Google Maps API, but you’ll need a couple of steps to actually grab and draw the boundaries. The Region Lookup API could somehow help you in the process of displaying the boundary of a region as it will return a matched place ID in its response, which you could then use to fetch the boundary data.

What you need to do is use the Data-Driven Styling for Boundaries of Google Maps JavaScript API to draw your polygon. You may view this sample from the documentation to have an idea of how its implemented programmatically. There is also an interactive demo on the documentation where you can try searching for regions live.

For more details on how to make it fully dynamic (i.e. applying Text Search (New) or Place Autocomplete), kindly refer to this documentation as it shows how to stitch all the API calls together so your users can search anywhere and see the boundaries.

NOTE: In the map styles, just ensure to properly enable the feature layers you require to avoid errors.