Should pans be washed before adding more poultry?

IMO, in a professional/commercial kitchen you should never re-use and always use clean equipment.

The risk of contamination is great(er) in case of chicken, so is the risk of having an inspector coming in and seeing dirty equipment lying around.

In terms of food safety, once a piece of equipment touches a piece of food, the equipment is that piece of food until it's been properly cleaned. If you put a piece of raw chicken in a pan, then take it out and wait several hours, that pan is still chicken that's been unrefrigerated longer than it should've been.