You sure can. However a fungal "wild yeast" contamination is far more likely, as that will take hold much easier. Most pathogenic bacteria prefer a less acid environment though (wort is slightly acidic). However if bacteria take hold, the by products are usually far more noticeable. You can have small fungal infections that you would never notice.
Especially slow fermenting beers with a high OG tend to be sensitive for bacterial infections. If your brew is infected it's likely already sufficiently inocculated before the yeast gets a chance to fight it.
You might even have a botulism infection in your mead or krausen ring if you are extremely unlucky. The few proteins/polypeptides in there are enough to start a small culture when they coagulate (krausen ring/foam) on your fermenter.
Should this put you off brewing? Nah. You are far more likely to win the lottery.. And as I still drive a Fabia I'm pretty sure that never happened to me either. It can also happen to dried sausage etc in a commercial factory.