Is it possible to go through the game without putting points into hacking?

Apart from boss fights, it is possible to complete Deus Ex: Human Revolution without anyone 'dying by your hand'. Doing so gets you the Pacifist achievement. Bosses don't count towards this however. Even with the alternative means of defeating the bosses provided in the Director's Cut, they still die.

Even at the start of the game, you will be able to hack devices that are security level 1, but there is no obligation to put points into hacking anything more sophisticated, at least for the main story. Locked doors etc. that are crucial to the story (but have a security rating of 2 or more) will have alternative means of going around them. Either you get the code from a datapad, get told the code or there will be a means of getting around it provided for you, such as an air duct. Without examining every objective, I can't guarantee this would be the case for side quests.

Bear in mind that nukes and stops cannot be used until you actually start the hacking process, which means you would at least need hacking in the appropriate level before you can use them. AUDs were not originally available with the base game (except by pre-order), so it should be possible to at least finish the story without them too.