If he takes them continuously - which is necessary to completely stop periods - then he will experience a "mock menopause", which sucks big time. The body gets addicted to estrogen based pills, coming off them is awful (painful) if they've been taken continuously. Citing my own experience here. Actually it was impossible to come off them cold turkey, I had to take 8 months to wean off them by dividing them up and taking less each day.
After the 8 months, my body - which had been used to a continuous supply of estrogen - had stopped making its own, so it experienced another 8-9 months or so of sex hormone deficit. This is also painful - the body doesn't have enough to repair damaged tissues quickly, becomes easily fatigued, bones and joints ache, and the psychological effects are nasty. Serious anxiety problems. On top of that it somehow affected my thyroid function which caused classic symptoms of hypothyroidism for about 5-6 months, weight gain, etc. I'm still living with some of the metabolic issues caused by that.
I definitely do not recommend using birth control pills to stop periods. If I'd known all the physical and mental consequences of taking them at all in the first place, I'd never have touched them. Doctors don't tell you these things when they prescribe them, that's for sure.