Dishwasher supply line is always under pressure, so the dishwasher solenoid can let water into the washer when you run it. Has nothing to do with clogs.
Paranoid (or prudent) people might turn that valve off if going on a vacation for more than a few days, along with the clothes washer line, if not the entire premises water shutoff. However yours is just connected to a Tee with no (before the) shutoff so not really done correctly, unless I'm misinterpreting the pic and the white cap on the end (far right side of the assembly) is a 2nd shutoff valve for it.