Private employers in California aren't supposed to inquire about arrests that didn't result in a conviction. That includes cases where defendants successfully completed DEJ programs (though there are a few exceptions, like applying for a law enforcement job).
There's always the chance that the court records will slip through and show up on a background check, but I wouldn't be to concerned about rinky-dink offenses like this ruining your career chances. Because I practice in a college town, I've handled innumerable cases like this and have never heard of a former client suffering lasting effects, even from a conviction. (Getting an MIP is almost a rite of passage at Chico State.)
The biggest danger is that a conviction on either charge will result in a one-year license suspension, which would show up on your DMV record. That could cause problems with jobs where driving is involved and would jack up your insurance rates. Successful completion of DEJ will help you avoid that.
Both of these offenses, Business & Professions Code §§25661 and 25662, can also be reduced to infractions. You might see if the court will reduce them before putting you on DEJ.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this site, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
When you enter a DEJ program you are not "convicted." A conviction occurs when you are sentenced and a deferred entry of justice program defers the conviction or sentencing. The hope is that you successfully complete the program and the judge dismisses the case. So if you successfully complete DEJ then there is no conviction.
If you were originally cited to appear and not arrested then an arrest will not show up on your criminal history. The citation may appear and if you successfully complete DEJ then a dismissal may show up.
It still stays on your rap sheet for law enforcement to view. The charge, date of charge, dismissed and the reaon for the dismissal.
Any answer to questions is not meant to be con screwed as legal advise and no attorney client relationship has formed. In order for an attorney to give legal advise, The attorney would need to have an opportunity to ask specific questions from a full and complete disclosure of the underlying facts involved in the question asked.