The point of the question probably should not be "should" - but should be "when". There is a lot going on in the police academy, sheriff's academy or the Highway Patrol academy. I did the LAPD route, however I have friends and clients that work for the other Law Enforcement agencies in the "BIG 3".
We always sit around and say who it better and that each other's training was on the level of something you might find inside of a "cracker jack" box as a Free Prize.
When it gets down to it - Each of the agencies mentioned - The Los Angeles Police Department - The Los Angeles County Sheriff's Department and the California Highway Patrol have some of the best training in the world for their Sworn Members.
While the "recruit" is going through the Police, Sheriff's or Highway Patrol academy - Real Estate should be the last thing on their mind. Focus, hard work and determination will all be the key to graduation.
After Graduation, the Focus, hard work and determination are not over - There is a Probationary period that must be passed by each of the Law Enforcement FNG's - for most, this period is 1 year.
After the Academy and Probation - Now is the time to "think real estate". I will tell you this and your Tax person will also let you know the Write off afforded to you by paying a mortgage (being able to write off the interest) - will be helpful.
Get with a Local Real Estate Agent - you will want to ensure they are established. Interview them and size them up and compare them with how they show themselves "on-line". You might be surprised....