In an in-person voting system, an individual must go to the correct polling place to get a ballot. It requires planning and preparation on the part of every voter. In a mail only system, individuals will receive ballots without making any effort at all. This brings up a number of questions, some of which can be adequately answered by the surveys from other answers. Others may be difficult to answer until after a major election is conducted using a mail only system, and then it may still be open for debate.
- Is it possible that individuals who would not go to a polling location would fill out a mail-in ballot?
- Will some people who wouldn't normally vote, fill out a mail-in ballot because a member of their household walks them through it?
- Is it possible that individuals who would never enter a polling place using someone else's name, would fill out the ballot of another voter that was erroneously delivered to them?
- Will some misdirected ballots be thrown away, preventing some individuals from voting?
- Is it possible that because mail-in voting requires less effort, that some people will actually be less likely to vote?
- Could filling out a ballot at home result in a voter making different choices than voting in a public place?
- The percentage of ballots lost in the mail should be near or at zero, but will it be a different number than ballots lost at polling locations?
- Could a delay in mail delivery result in some ballots not being counted?
- Will provisional balloting be more or less accurate in a mail-in system?
- Would a mail in system be more or less susceptible to 'stuffing' by a nefarious individual or group?
- Without in person exit polls, will there be any observational data available to correlate with the official results?
A mail-in only system would be different than an in-person or hybrid system. Any change at all to the voting system would result in a different number of total ballots counted. A different number of ballots could mean different percentages for certain candidates or initiatives. But whether the difference would be significant or actually change the outcome of any particular race seems impossible to prove - even after the fact.
What could be stated with more certainty is that regardless of the balloting system employed during the 2020 election, in the after math, both major US parties will claim that the other took advantage of the current pandemic and cheated somehow. And most likely, one party will claim that the election was stolen by the other. In such an unsettling and unpredictable year, it's nice to know that there are still some things we can count on.
Edit:
The question is about whether mail in voting would help the Republican party. The other answers cite studies the suggest changing the voting system would not affect the outcome of the election. These questions posed above are NOT answered by the studies cited. The primary point of my answer is that in fact, we don't know the answer to the OP's question. Pretending that we know may bring comfort to some, but the studies are not definitive and do not claim to be. The study in the most accepted answer states:
We find that 1) universal vote-by-mail does not appear to affect
either party’s share of turnout, 2) universal vote-by-mail does not
appear to increase either party’s vote share, and 3) universal
vote-by-mail modestly increases overall average turnout rates, in line
with previous estimates.
Each individual is free to interpret the meaning of 'does not appear' for themselves, but by any reasonable standard it means that the study is not conclusive. The study shows a 2% increase in voter turnout, but the only offered explanation is that it is consistent with conventional wisdom and other literature. They did not definitively determine why more ballots are counted in VBM.
The study also has 3 caveats. The third doesn't apply to the OP's question as it is about VBM only. The others are important.
First, our evidence is about the effects of counties opting into
universal VBM programs during normal times—that is, the counterfactual
we are comparing voting-by-mail to is a normally administered
in-person election. The effect of VBM programs relative to the
counterfactual of an in-person election during COVID-19 might be quite
different, and the effect would depend on whether we believe COVID-19
disproportionately deters Democrats or Republicans from voting...
Second, our results say nothing about whether VBM should be
implemented nationwide. There may be reasons to worry about rolling
out nationwide VBM that we cannot study; for example, it might have
disparate impact on minority voters, who, some claim, utilize VBM at a
lower rate...
So clearly, they aren't sure if implementing a mail-in system for 2020 would impact the outcome of the election. The study is good and is the best information we have, but it is not definitive and there are many questions which have not been answered. The only thing it actually proves is that more ballots are counted in VBM. My answer is, it will be different as proved by every study ever done on the subject, but no one really knows if one party would benefit. It is either unscientific or disingenuous to pretend that we do.
Edit2:
After these results in Michigan, it seems clear that we should consider human nature in addition to conventional wisdom when considering how mail-voting could be different. From the article:
- 6,400 of Michigan's 10,600 absentee ballots rejected Aug. 4 were turned away because they arrived after Election Day
- 2,225 ballots were discarded because there was no signature on the envelope
- 1,111 were rejected because the voter moved
- 846 were not accepted because the voter was dead
- In the November 2016 election, 1,782 absentee ballots were rejected because the voter had died
- the U.S. Postal Service has warned Benson that Michigan's mail delivery timelines pose "significant risk" to ballots sent too close to Election Day
A few of the questions above have now been answered definitively. And this new information begs other questions:
- Were there other anomalies that voting officials were not able to discover?
- Will all regions be as vigilant in disqualifying incomplete or illegitimate ballots?