I would not mind this even if it did an automatic deposit of all cash on hand you have into the bank. Here is why.
For simplicity sake there are really only 2 kinds of players as it relates to this proposal, those that schedule sleep time after a job (Or after 2 or 3 jobs if they have premium) and those that don't. AS a subset of both of those you have those that have premium and those that do not.
So if your a person who does not go to sleep after a job and whether or not you have premium nothing is really going to change. You will still be out there being able to be targeted by a dueler. In this case the change to duelers is negligible.
If your a player that goes to sleep after a job and do not have premium, then that means you do 1 job then go to sleep. So the only time a dueler can attack you and get cash is on your way back from the job. Again nothing will change except that the dueler will still be able to challenge you after you make your deposit. That means that the dueler actually has the benefit of challenging you more often. +1 for duelers! In reality I doubt non-premium sleepers would change what they are doing much even with this, but in the end it's at a minimum a draw and at most beneficial to duelers.
Now take the case of a player that sleeps after a job and has premium. What do they do now? Do 1 to 3 jobs and then schedule sleep time so they can deposit when they come back. I can see this changing slightly in that they will still do 1 or 2 jobs, then go deposit then go do another job or 2. So this means duelers will have more time to target those players as they are traveling and awake instead of sleeping. So a dueler is not likely to get a better chance at gaining any more money, but they will have the benefit of having more targets to hit more often. So I still see this as a benefit to duelers.