No, all "research" does not point to that.
For goodness sakes, after years of denial, since the advent of free market neoliberalism, this has been the claim, that adding more and more low end workers has no effect, and it's bizarre now to hear the supposed left pushing it. Even the IMF has now allowed that wages are affected in this way, and while the degree to which that's the case varies, that's not something that can be hand-waved away. It's also allowed governments to neglect education and skills development among their own population.
Similarly, these organizations are now admitting that whether an immigrant adds more to the economy over his or her lifetime depends on what kind labour they are doing. Which shouldn't be a surprise, it reflects the nature of jobs within the country generally.
The fact that adding, say, 500.000 new people to a population requires that many new homes and new doctor's placements is obvious, unless you are ok with not giving newcomers adequate housing and medical care. Not only is that an up-front cost, it's not easy to simply increase housing stock or health infrastructure, it takes time. In Canada, the national bank recently, and in a shocking reversal of the neoliberal narrative, warned that large amounts of immigration were causing increasing inequality and destabilization in housing, and masking a weak economy.
None of this means immigrants are bad people, or there should be no movement, or anything like that. It does suggest that the experiences of low wage workers, and the people on the low end of the housing market, were not just racist figments of their imaginations as the capitalist right claimed, and the middle class, bourgeoisie left are now so keen to insist on.
As long as the left is insisting on that narrative they are not going to win the trust of the working classes. They can claim to be righteous leftists all they want, but if they talk like neoliberal global capitalists, and act like them, a few social programs and "be kind" rhetoric aren't going to convince anyone otherwise.