It might make some difference if it removes a hoop or two they no longer have to go through.
There's also a third reason why young people (or anyone) might not vote - pure apathy or any sense of civic duty at all.
Where does the apathy come from? the biggest influence is family and friends. as you say it's not just young people who are apathetic and if they hear people close to them telling them they are all the same so no point voting then I can understand why they believe this. it's actually the older people who hold these views for life that are doing the damage. I don't mind voters being put off from voting Tory it's being put off from voting Labour believing they will do nothing for them which is wrong, don't get me wrong, young people have been let down for years and we know the reasons why governments have done this, they know young people won't turn out in force to punish them, it's a self fulfilling -prophecy.
One of the most stupid damaging statements Corbyn made as leader was to make a video 6 months before the last election saying all governments in the past 30yrs or so have ignored you, meaning the last Labour government ignored you.
It's as if he didn't even consider his job is to convince people to vote Labour and here he is saying the Labour party ignores you. Momentum went around the council estates asking young people to vote, walked up to a crowd of young people standing around and asked them if they would vote Labour, nahh we won't bother voting, no point, they won't do anything for us. that's what never seems to register, spending years attacking Labours image while fighting to take over Labour, they finally take over the party and do a complete u-turn and now it's please vote Labour, why the surprise when people say nahh you all ignore us so what's the point.