Can my a bad batch of beer poison me?

No.

There are no known human pathogens that can survive in beer. The alcohol and relative acidity help to protect it. Infected beer may not taste very good and you may not want to drink very much of it, but it won't make you sick per se. Of course overconsumption of beer can result in temporary sickness and nasty hangovers, so drink responsibly and know when you've had enough.