I would like to try out here's Maps API for JavaScript. Unfortunately I am tied to another base map for now. Can I use here's Maps API isolated from here's Map Tiles?
It all depends on what you're using the Here API for. If you're using features that don't depend on the map tiles, you're free to use whatever other maps on your application you want (e.g. routing/places/traffic/etc).
I'd probably recommend using the REST api: https://developer.here.com/develop/rest-apis
Of course you're free to use the javascript api for the same purpose. It just wraps these in js object.
If you're looking to do things like creating map objects and customizing the map, you can't use the here api. You would have to do that using the google maps api if you're using their tiles.