Your question is a bit confusing.
iTunes Match is completely separate to an iPod Nano, its not meant to work with it at all. It has no ties, relation or impact to how the iPod Nano gets its music at all.
iTunes Match allows internet capable devices signed into to your Apple ID to access any music that was matched or uploaded to the service over the internet.
The iPod Nano does not connect to the internet, nor can it access iTunes Match in any way whatsoever.
The iPod Nano gets its music from the computer it is synced with, the same computer that should have that same iTunes Music library that was synced to iCloud through the iTunes Match service.
The computer that holds your library can sync the songs to the iPod Nano regardless of the iTunes Match existence.
Any music downloaded from the iTunes Match service to the iTunes application or the Music App on a Mac will then be able to be transferred to the iPod Nano via a regular sync.
iTunes Match does not DRM protects your tracks and once downloaded can be used with an iPod Nano.
If you are using the Apple Music subscription instead of iTunes Match (different and separate subscription services), then music downloaded from there is DRM protected, and would not be transferable to the iPod Nano, but should not really matter, if the computer you sync the iPod Nano with still holds your original and unprotected tracks and albums.