Yes. If you have successfully set up the Id as a MC Server, and transferred the MC Library from your original Windows 10 machine which was acting as a MC Server to the Id, then on your new Win10 PC under Library Manager, Add Library, give it a name so you can identify it as a Client of the Id Server, then with Library Server selected, enter the Access Key, click Ok, and you are done.
MC should connect to and open the Library on your new Id Server. Actually, it copies the Library from the ID Server to the Windows 10 machine each time you open the Client, and it synchronises the Libraries while the Server and Client remain connected.
The Playlists you have on the Id Server will appear in the Windows 10 MC Client.
The above is assuming that I understood what you have set up correctly. That is, the Id is now your MC Server with a current copy of your original Library on installed. It connects to your NAS for media files, and you control it with JRemote. The Windows 10 PC you are attempting to connect to the Id will act purely as a MC Client, for playback of media from the NAS locally ("Player", under Playing Now), or to control playback of media on the Id ("There", under Playing Now).
Note: If you were actually talking about Playlists that exist on your original Win10 machine, and not those already on your Id, let us know and we will sort that out. It should just require a Library backup from your Win10 machine, and a Library restore on your Id, but since the Id is UNIX, there may be some issues, such as the path to the media files. But if you are using a NAS, you should be okay, depending on how you address the media files. You may want to search the forum for how to move a Library from a Windows PC (your original MC Server) to an Id if you haven't already done that.
Note also that any Playlists created on your new Win10 Client will need time to synchronise to your Id Server. So you can't just create a Playlist on the Win10 Client, immediately close the Client, and expect the Playlist to be on the Id. You will need to either wait a few minutes (usually it is just a few minutes, if not near immediately), or manually sync the Client to the Server, also done under the Library Manager or Playing Now.