Do alien Greys implant hybrid fetuses in human females and allow them to be carried to term and raised as humans by these unwitting mothers as part of an infiltration of human society?

This indeed is happening as you have seen intuitively. It is the ultimate enslavement of humans, to raise the young of the extraterrestrials, do all of the work, and to be exploited in the bargain. This is a clever co-opting of human nurturing capability, to provide what the human part of the hybrid beings need to cultivate their human qualities and maintain an inner emotional balance, as they are human enough they need love. And this is one of the purposes for the hybrid experiment, to incorporate human characteristics within the lineage. So these beings are being introduced as a means of furthering the agenda of the Greys to make as much progress as quickly as possible in their genetic program to form the ultimate hybrid. So they are using this strategy to speed things up. At the same time, they are also commandeering families to serve them as breeding centers and not breed new humans. This serves them in moving things toward human extermination. This also positions the hybrid offspring among the human population so they will have the greatest chance of being accepted without question and will be able to infiltrate all levels of human society eventually, and with greater numbers can become a force to reckon with, capable of subterfuge, sabotage, and a kind of guerrilla warfare should that be advantageous for the interlopers. So this is a program with multiple agendas, none of them serving humanity.