Vote-by-Mail (VbM) is the way to go, and has made a much larger difference in terms of registered voters actually voting in Oregon (We were the first State to enact), and certainly compared to the relatively minor effects of Automatic Voter Registration (AVR) in Oregon.
VbM will likely have an even bigger impact in Arizona than many other Western States, simply because of relatively low voter turnout rates.
Now, one could postulate about the partisan impacts of increased voter turnout levels in Arizona, where items such as VbM tend to increase turnout among younger voters the most (<35), as they did in Oregon.... In Oregon, I have yet to see any real evidence that it dramatically altered the political landscape between 1988 and 2004 electorally speaking. Maybe Gore would have only won Oregon by 2% in 2000 and Nader might have performed slightly worse, but the fundamentals were already baked in, and Middle-Aged and Middle-Class voters in Portland & the Suburbs, as well as other similar communities throughout the State, would still have swung hard against the Republican Party.
Because of the demographics of AZ, one might imagine that Democrats would be net beneficiaries of VbM, as well as the reality that Millennial Voters generally don't like Trump at all.... In 2020, one could potentially foresee some of the '16 3rd Party Millennials in AZ voting Dem, without HRC at the top of the ticket...
Still, Millennial Voters as the major beneficiaries of VbM, might well continue their heavy 3rd Party voting streak in '20, as a generation that is both heavily idealistic, but also extremely disillusioned with the current state of American politics.
When it comes to statewide non-Presidential Elections, the key is will this surge of newer voters vote for down-ballot contests as well, or just stick to top-of-ticket?
Either way, I would imagine the surge of new voters would likely lead to AZ voting Green on MJ legalization, and quite possibly will boost '18 voter turnout that could impact the '18 AZ-US SEN election, even without VbM.