In my experience with the non-classical app, Apple Music has good but not perfect support for a local/offline library. I'm not sure, but you can probably do loc

In my experience with the non-classical app, Apple Music has good but not perfect support for a local/offline library. I'm not sure, but you can probably do local playback of offline music even without a subscription. If you do have a subscription, it will actually let you upload your local library so that it can be streamed to any device (e.g. upload on PC, stream on iPhone). The two imperfections are that it's limited to AAC quality even if you upload a lossless file, and that it will sometimes "match" your local file to something in the Apple Music Library, and it's not an actual perfect match.