If the city connection water pressure is lower than the pump cut-off pressure (usually around 45 PSI) then it will run when a faucet is opened. However, when connected to city water the pump should be turned off. I have never seen an RV that had the pump hot-wired into to the system with no way to turn it off.
Chuck - Sparta, TN
2012 Jay Flight 22FB, 2 x Honda EU2000i
2013 GMC Yukon XL Denali AWD
EDUCATION is what you get when you read the fine print.....
EXPERIENCE is what you get when you don't.