Unless they can kill the electoral college, the illegals are basically in dem states anyway. Minimal effect on national elections.
South Carolina, a Republican state that has seen an increase of illegals at a rate of 48% over the past year. Add their off spring to that rate and it takes no time at all to take over...
Texas is not a Dem state. Neither are most of the great plains states, all have significant populations of illegals. Plus there are a lot of illegals in states that are "swing" states, like Florida, which would be driven into the 'rat column.
But it's the swing states where it would matter.