I don't wash my eggs (the rare super-pooey one goes into compost, slightly pooey ones are eaten right away); I don't even always refrigerate them, they don't really need it except in hot weather or for longer storage.
For vacation, there are sort of two questions, one is "what can you sometimes get away with" and the other is "what gives you good insurance against problems".
In terms of a smart plan that makes tragedies or lingering unmanageable problems unlikely to arise, you'd want someone to check on the chickens once a day and collect the eggs.
In terms of what can you sometimes get away with, <shrug>. The two most important issues involved are:
--egg eating developing as uncollected eggs pile up. Egg eating cannot always be cured (except by the stewpot) once it has become a habit.
--waterer or feeder getting spilled/emptied. Just a day without water will seriously affect chickens' health; more than that, and you will probably not have a flock to come home to. Running out of food is not as dire but the less food, the more chance of cannibalism, which even the cutest friendliest chickens have no reservations about engaging in.
and there is also:
--if nobody is checking, then nobody will notice and FIX IT if a predator starts to dig/gnaw a hole into the run or coop, or the coop/run get damaged in some fashion that creates a weak point for predators to get in or chickens to get out.
--if an injury or illness occurs, nobody will be there to treat or isolate the victim and it can progress into a far more serious situation -- a common scenario woudl be a hen getting pecked or partially prolapsed, which is eminently curable if you catch it right away but if you leave her in with her flockmates for several days they are pretty likely to kill her gruesomely.
It is not like checking on the chickens is a complcated thing -- if you have large waterers and feeders, probably all your "chicken sitter" has to do is collect eggs once a day and make sure nothing has gone wrong, although obviously you should leave instructions on how to deal with any problems that might arise -- so personally I do not think it is fair to the chickens, nor prudent as a chicken-owner, to leave them untended for longer than a day. Your mileage may vary of course.
Good luck, have fun,
Pat