Primary radar has bad accuracy in altitude. It has many blank spots and gives returns on anything from birds to kites etc and it suffers from clutter, interference, noise etc. It's not a very accurate tool (in altitude at least) and that's precisely why they came up with secondary (SSR) radar, i.e. the transponder that answers back with vital altitude information (that, by the way, can also be rigged by feeding the SSR system the wrong info, if one was so inclined).
An official disclaimer as some here seem to think I'm cheering mavericks and endorsing law breaking. Nothing could be further from the truth. This is not something I plan to use or will ever try unless I was forced to by extraordinary circumstances (my country gets invaded and I need to escape, or fear of death etc).
But the hypothetical argument is interesting and a valid discussion.
It would be entirely possible to take off from a private field, fly under radar, pop up in the no fly zone, set off the alarm, drop down again and land at said field without anyone ever being able to know what aircraft had done so. How do I know this, because I have some acquaintances who, shall we say, did bust R-zones in the US, got 90 day suspensions and then preferred to leave the transponder off in their subsequent flying and have after that inadvertently bust R-zones again and had suspicions brought on them but upon questioning they couldn't prove it wasn't a malfunction or that it wasn't something else giving a return or give a more precise altitude. This is in military R-zones, where according to SoCal, all the equipment is so sophisticated they know if you're circumcised or not.
My subversive nature leads me to think that's exactly what they want you to think, as it keeps people in check, but I'm not so sure that's actually the case.
When the next Hitler comes along and invades my country, my escape will be flown low, with the transponder off...