This assumes that the vast majority of the illegals to sway those representatives only benefit democrat candidates.
C'mon man.
It matters how many, and in what states they live when they answer the census. If illegal immigrants are counted towards apportionment for EC/House representation, then they damn sure can give democrats an advantage. Looking at the top 10 states for illegal immigration (California, Texas, New York, Florida, Illinois, New Jersey, Georgia, North Carolina, Arizona, Virginia, in order of population rank). California, Texas, NY, are probably the only states with a high enough illegal population that could change apportionment. So yeah, Texas could pick up some Republican representation (assuming that districts would be drawn such that it would favor Republicans). Would it make a big difference? Not huge, but could give Dems a several seat/EC delegate net gain, making the EC path ever more difficult for Republican presidential candidates.