Boot Loops with bad battery

I have an iphone 5 that I don't know the history on, that I bought off of ebay. When I first try powering it on, it boot loops if I plug a charger in it will sometimes boot but will reboot once in awhile.

I removed the battery and connected a power squid, and the phone does boot just fine. I also tried removing the power squid and connecting it to a charger and it boot loops again.

My question is should the iphone be able to power up with the charging cable and no battery. Just looking for info to see if I need to go further than just replacing the battery. I know the battery is bad because when connected to my power supply to charge it pulls high current and then the current drops and just continues doing this.