Mark is really destroying ARAM. It used to be a game where poke was dominant but there was still a place for tanks and AD carries. Some champions were bad, but imbalance is unavoidable. Mark doesn't just shift the balance, it obliterates it. Close range skills are strong because they should be tough to pull off, but Mark's cooldown is so low that you can just spam it until someone gets hit (no full team of 5 is dodging 10 snowballs a minute), then press whatever win button you have, usually something with aoe CC. There are many champions that do better in sustained fights, but those no longer exist in ARAM. One or multiple people get caught, then Mark allows for the stragglers to easily be picked off. 2-3 people running or under a turret are probably going to get marked and will die to a 5 person tower dive, or else watch the turret die.
Basically, Mark changes the champion balance, at the very least in a neutral way, but in my opinion in a bad way. On top of that, it accelerates the game too much. Comebacks are far less likely when your team can't even survive to wait for friendly respawns. Farming minions on the losing side is now even more impossible because not only are you constantly dodging the enemy poke, you're now dodging snowballs that lead to instant kills. It's also exploitable by champions like Annie and Lissandra, who were already strong ARAM champions before, but are now capable of powerful hit and run tactics that are difficult to punish. The scale of champion strength went from 3(weak) - 5(strong) to 1(free kill) - 7(press Mark to win).
TLDR: Does Mark stop the 3 poke, ADC, Sona team from winning the majority of games? No, it just adds more ridiculous combinations. The more ridiculous champ combinations in ARAM, the more it suffers. ARAM is fun when team composition isn't the major factor in whether or not you win. With limited rerolls, it's still common to have "crappy teams," but there are more winning lottery teams, meaning even more games where you lose at champion select or want to surrender at 5 minutes.