YES, a hose that feeds water at the bottom of the tray helps with water changing and circulation. You can also buy them at medical supplies, people with disabilities use them to have a "hand shower" in the bathtub spout.
IMHO it would work even better if you had 2 trays, the one you show and another one in "cascade". Run-off water of the top goes to the bottom one.
Prints go first to the bottom tray, then to the top, then to dry
That way you make sure the cleanest water is nor recontaminated with "dirty" prints