Again, aside from cost and legalities - even in the height of the cold war where budgets were seldom an issue, I can't recall any of the militaries around the world doing basic training in multi-engine aeroplanes. It was always in a single - sometimes a jet, but still a single. (I have a friend, ex-US Navy who never flew a piston engined aeroplane until Test Pilot School, and I don't think ever logged PiC in one.)
I'm sure it's legally possible: the pilot would end up with an MEP but not an SEP rating, and it would take longer and much more money; I'm sure you could find an instructor who'd do it for all of those lovely juicy multi-engine hours - although I hope they'd have the grace to try and talk you out of it first.
G