iTunes Match is a subscription service that allows you to sync your music collection across all devices that you add to the service. Songs are either "matched" or "uploaded". Matched songs appear much like they do if you have purchased them, in fact if you delete a matched song from your device, the copy you download will be the full DRM-free 256kbps version of that song from iTunes.
Without the subscription service, Apple still makes all previous purchases available to you. It knows you have purchased them and allows you to re-download them. In this sense you are getting part of the iTunes Match service but it only works for songs purchased from iTunes.
Show All Music does exactly that. It shows all your music whether on the device or in the cloud. Turn it off and you only see items that have been downloaded to your device. This is really handy when you are offline. Nothing worse than trying to use your iPhone to play songs that are still in the cloud when you are in airplane mode.
So to answer your question, you need to turn on iTunes Match to be able to see your non-downloaded songs that were not purchased from iTunes or did not "match" songs in the iTunes store. Once you have downloaded everything you can turn iTunes Match off if you like, but every time you turn it on again it "replaces" the music on your device with what is in iTunes Match.