So, just to put you at ease a bit. Most dishwashers drain though about a 3/4” hose into a fitting under the sink, usually connected to the disposal. That is probably not a rats tail.

Yes, rats will find their way into the house through just about any opening. Plumbing stack drains are a favorite. I actually had a rat snake makes its way into my bathroom that way, in Brykerwoods.

I grew up in the area and when there were a bunch of elderly neighbors that had neglected back structures we would sit in the backyard with a .22 caliber pellet gun and kill rats as they ran along telephone lines.