I dated a guy who went through all the tests, the interviews, and the meetings and such. He never made it in, his letter of rejection told him it was because there were too many applicants and not enough spots, so, although I have no advice on what it's like to know a cop / be with a cop I do have advice on the process!
Straight up, you should NEVER lie, even if it's not during the polygraph. My ex's parents drank a lot and as a result all of their underage kids were allowed to drink. That never came up in the polygraph, but, it did during the medical examination. The doctor asked if he drank and asked if he was 21 or not (he was not). Then he asked why he thought it was ok for the underage to drink, and my ex gave a pretty good reason (and it was true) that he only really drank for special occasions and he didn't see anything wrong with it as long as he, nor was anyone else, driving afterwards, and, that he was not recreationally drinking, it was to celebrate an event.
I would say that if your SO is overweight that he should loose the weight before applying. You can only appy once a year and my sisters ex applied last year. He's 250 and he does not carry the weight well. He did not get asked back for an interview, something that they ask for in no time after the written test. After each process you are contacted pretty fast to meet again / do something in the process again. You'd never go over a week without knowing information as to the next time you're supposed to meet someone / do something. There were also, as I remember 2 times when he had to go running with a group who was applying as well and keep up with everyone.
The process is pretty quick, it took my ex when he applied in Sept all the way to Dec to his final interview. It's just long to weed out all the people they don't want in the force and to get rid of the people who can't / they don't want in there.
Hope I was some help! GL to him!