"...I have studied what happens to one's DNA in advanced college courses."
My DNA never got to take "advanced college courses" so nothing has happened to it. :)~
Joking aside, if I'm understanding your question correctly then No, Ancestry's Autosomal DNA (atDNA) test does not also include a Y DNA (yDNA) test.
If you're interested in yDNA testing I'd suggest going with FTDNA. While Ancestry is more or less leading the charge with regard to atDNA testing it's yDNA participation is weak at best.