Is it normal that my phone reboots without battery?

I got myself iphone 4 without a battery, I want to buy one, but I’m not sure if I should. I connected it directly to psu (as battery connector was already ripped), and it boots and works fine for like 2 minutes and 20 seconds, and then screen goes dark and it reboots. Is it normal for an iphone without a battery(or rather battery attached only to positive and negative terminals) to do that?