In a previous post I argued that the answer is no:

I don’t believe that immigration will make America more diverse, nor do I think it will make the electorate vote more Democratic.  That’s because immigration from Asia and Latin America has made earlier immigrants from southern and eastern Europe seem less different, more “white” than they seemed in 1924, when immigration was restricted because America seemed to be becoming extremely diverse. By the 1950s, that same ethnic mix was viewed as homogeneous.  Intermarriage rates are now so high that the day will come when both Asians and middle class Hispanics will be viewed as culturally “white”.  Fifty years from now America will still be about 75% “white”, in terms of people’s perceptions. (The black population will stay around 13%)  Diversity is a state of mind.

And as immigration brings in people who don’t vote Republican, it makes existing residents more likely to vote Republican.  Thus each party will continue to win roughly half of the vote.

Tyler Cowen directed me to an academic study from 1998, by Amihai Glazer, Bernard Grofman and Guillermo Owen, which supports my claim:

We extend the standard Downsian framework to suppose that voters consider the identity of each candidate’s supporters when deciding whom to support, rather than considering only the announced policy positions of the candidates. In particular we posit the existence of a class of voters whose support for a candidate reduces support by some other voters for that candidate. Our most important result concerns the conditions under which the addition to the electorate of new voters on one side of the policy spectrum shifts the equilibrium toward the opposite direction. The model can explain why enfranchisement of blacks did not immediately help the election of liberal candidates.

I recall when civil rights advances in the 1960s made it much easier for blacks to vote in the South.  Most blacks voted for Democrats, but the states where they lived actually swung toward the GOP after 1964.

We are seeing the same thing over much of the developed world.  Immigration is associated with a decline in left-wing parties in places like Germany, even though the immigrants themselves tend to vote for the left.  Indeed in Germany the AfD recently surpassed the SDP in polls, a situation that would have seemed unthinkable just a few years ago.