tl;dr : No, DotA 2 doesn't support yet custom game mode.
DotA 2 is a full online game (Appart for some tournament where players play on local lobby). This means that the game settings are set on Valve's server and thus can not be changed. Either you play All Pick, Captain's Mode or ARDM you can not turn off deny when playing matchmaking. Even if you create a private lobby, there are no option implemented at the moment that allows such thing.
However, with the release of Source 2 coming early 2015, DotA 2 is on the way to fully support custom games modes which could lead to DotA games where denying is turned off. Still this would not be an official DotA game and you might not find many players to play with you.
That being said, learning to deny is a concept inner to DotA. If your friend has trouble denying he can use the folowing command dota_force_right_click_attack "1" which makes denying a lot easier since you can right click to deny and are not longer required to press the Attack key then select the creep you want to deny (This command can be written in an autoexec.cfg file so you don't have to type it everytime you start the game. If it's the whole concept of denying that is the issue then I'm afraid there is not much more you can do, denying is a part of DotA and is a very interesting game mechanic. It can help you control your lane (if you want to push or not), it forces you to decide if you want to commit for a tower kill or if you let it being denied, you can even do some clutch plays and deny allies when they are low life thus denying some much needed XP and Gold to the enemy team.