Can this work as an ADC Input setup and is it common?
Yes, it should work although there are some issues to watch out for.

The tricky issue is that you have to be careful to detect and ignore the transistions between the 0 V switch level and the pot level.  Some of them are going to look like valid pot levels, so you have to take multiple samples into account to decide if what appears to be a pot level is real or just a intermediate voltage while slewing between the switch and the pot.  Keep in mind that real switches bounce, so this is more tricky than you probably imagine.  One thing you know about a valid pot voltage is that it can't change that fast.  This should help in weeding out intermediate readings.

Another issue is that you can't read the pot when the switch is pressed.  There is nothing you can do about this with this setup.  Whether that matters depends on the system and what the meaning of the pot position and a pressed switch are.

I can't say whether this is done "often" or not.  Pot inputs by themselves are unusual, but of course they do exist.  For this scheme to make sense, you have to have a system that needs both a pushbutton and a continuous setting from the user, and where you really really don't want to spend the extra pin.  If this is the difference between fitting into a 28 pin micro or having to use a 44 pin micro, I'd probably do it.  If I have other pins left over, I wouldn't do this because it's better to keep the complexity low.  Separate pins for the pot and the button are going to be easier, and therefore less likely to have bugs, in the firmware.