Even though I don't use wax currently, although I've switched to the Rock-n-Roll Gold as an experiment on the velomobile (so far, so good) I always clean/lube my chains either after a ride (normal maintenance spray/wipe) or on the weekend when I know I won't be riding for a bit. Even a lot of lubes that say it doesn't matter seem to work better if allowed to set and evaporate before riding.
My experience is based mostly on years of commuting in AZ, where there is year round dust, and only occasional rain. I did it the same way when I lived in Seattle though, and I can usually get 6-7k miles out of my chains no problem.