I've perused this board for years, but have never bothered making a profile since I don't know much about wrestling and thus can't really add anything meaningful to the discussions.
Aside from being a massive sacrifice and basically requiring you to take two years off from practicing your sport (as HOA242n! described), one cannot simply decide to go on an LDS mission one day then leave the next. You have to be a baptized member of the faith for at least a year to be considered. Even then the process of applying to go is an onerous, months long process that includes interviews with two layers of clergy where you would have to convince them you actually believe the church and its doctrine are true. As well as attest to the living of its rules, IE no coffee or alcohol, paying a 10% tithe, chastity rules, etc.
This on top of what HOA242n! describes as an extremely taxing, regimented and dedicated 2 years of service.
So I could be wrong, but I don't think Cole and Henckel would be going on an LDS mission, although I'm sure they will do a whole lot of good no matter what mission program it is.