Yes. Learn to monk split. 2 monks can't heal you twice anyway 
Just make sure you click them, they will follow them around everywhere, though they are prone to tower suiciding. Also, if your tagged player gets a kill, you will typically get an assist, and your monk will also grind a small amount of XP / Gold for you. win-win. Your partner stays capped hp, can hold lanes better, better warscore... you get assists, slight xp/gold boost.
You lose nothing, really, except having to be very careful not to lose your only remaining monk...