Can Rhys be played in a mono-green EDH deck?
No, you cannot play Rhys the Redeemed in a mono-green EDH deck. You can only play cards with hybrid mana costs if all of their colors are part of the commander's color identity.

The commander rules describe the color identity rules in rule 903.4:


  The Commander variant uses color identity to determine what cards can be in a deck with a certain commander. The color identity of a card is the color or colors of any mana symbols in that card's mana cost or rules text, plus any colors defined by its characteristic-defining abilities (see rule 604.3) or color indicator (see rule 204).


and the hybrid mana symbols are defined in rule 107.4e:


  Hybrid mana symbols are also colored mana symbols. Each one represents a cost that can be paid in one of two ways, as represented by the two halves of the symbol. A hybrid symbol such as {W/U} can be paid with either white or blue mana, and a monocolored hybrid symbol such as {2/B} can be paid with either one black mana or two mana of any type. A hybrid mana symbol is all of its component colors.


So, Rhys's color identity is green/white, which means that it can only be played in a deck with a commander that has both green and white in its color identity.