Even if you recorded it as installed, it would be difficult to record it ever being uninstalled because the event that prompts you to install it is the only way you could ever determine that it was uninstalled. However, they could have 2 devices and install it on one but deny it (or ignore installing it) on the other. Then, it'd be recorded as uninstalled, all the while they still have it installed on 1. Unless on opening the PWA it "installs" again, but then when they get on the other device that they denied it, it would be recorded as "uninstalled" a further time.
That's my understanding of how PWA works though.
It could be possible, but I do not see how it could.