The best way to check is by using
Time Warner's channel lineup webpage and entering your zip code or city and state. I searched for my state here in Arizona, and their basic cable service only offers the main local channels (like ABC, CBS, FOX, and NBC), not their subchannels. This may vary by city and state, so don't take my word for it.
If they don't offer subchannels, you will need a converter box, and it will have to be connected to your TV independent of your cable connection (using an AB switch or a splitter).
Do you have basic cable service with Time Warner or do you rent one of their set top boxes?