Yes there is a connection; some illegal aliens vote and almost all who do no doubt vote democrat.
But the population of democrat-voting legal immigrants (and their first generation children) is much larger. Unending mass legal immigration is the much bigger demographic threat to conservatism. Drastically reducing legal immigration and ending this era of mass immigration is just as important to achieve as are the actions against illegal immigration like border security, deportations, and cracking down on sanctuary cities, maybe more so.
Of course the two are very much connected thanks in large part to the disaster of birthright citizenship and anchor babies. That needs to be abolished too.