If you aren't already working on doing push ups, then, no, 10 or 12 isn't realistic for anyone.
It's a silly premise. It's like saying if you can't run 5 miles, or bench press half your body weight. If you don't do that thing AT ALL, then you can't do a benchmark of that thing. Sure, a fit, fast regular walker or hiker might manage a first time 5k run, stuff like that, but generally "can you do X physically exerting thing?" maybe not, but that doesn't really mean anything bad in and of itself.
If you haven't tried a push up in 10 years, chances are you can't do a dozen. If you trained and worked on them for a month or so, then, sure, you could.