I don't think it's allowed, but that is possible and probably against their terms of service.
I would maybe do it with a brother or close friend, but you have to be careful if a console dies on you that you de-activate it before getting another one.
Also I'm unsure about if you could both play online at the same time on the same game using that method, if that does work then yeah would be worth doing for cheap games but only with someone you trusted as they would have the password to the account, etc as well as access to the registered credit card, etc.
Just don't give them the Amazon account password, and only tell them the PS account but yeah the main thing is if you can both play at the same time I read once downloaded you can log out and into your proper account and play it so id hazard a guess and say it's possible to both play online at the same time and it could be ridiculously cheap.