15 minutes is pretty rough for a first dodge. Especially if/when the client bugs out.
Rather than increase the dodge timer, some sort of memory should be there like someone dodges, next game everyone gets the same champ as they did last time, until the match is made. Then dodging would lose appeal because after the timer was up, you would still get the same champ you dodged because of. So many times, I have a champ I am excited to play and someone dodges. New lobby, another champ I like, someone dodges..
Maybe it would kill aram, maybe it would help it.
I'm pretty confident just about anyone who spends a decent amount of time in aram has an "aram" account.
Regardless of the timer though, that will never be a true deterrent imo. Dodge timer increases, we just make another aram account. Most people, I personally know, who play aram have 4 or 5 accounts. Now get 2-3 people in a premade who have that and you can take turns dodging games w/o true penalty for 10-15 games in a row if needed.
Unlocking the full champ pool has been mentioned in the past which would also be a good idea to combat aram accounts, but ONLY IF they unlock rewards for champs you don't own also..