Is it possible to use a milling machine *bit* in a drill press?
Mills and drills are not just random chip makers. They are totally different, and for good reason. 

End mills are designed to work off the ends of the tool, i.e. they are driven laterally into the work. They are built for this kind of shear stress, and not to be driven axially.

Drill bits are designed for axial forces not lateral ones - they fall to pieces when driven laterally.  And drill bits have a vital feature end mills do not: the ability to cope with the varying tool speeds radially, and particularly the ability to drill in the center where tool speed is zero.  End mills simply are not made for that! 

So you say these things are "the reverse of", they are not the reverse at all.  Using an end mill in a drill press is a completely different kind of operation than using a drill in a mill.  An end mill in a drill press doesn't make a whole lot of sense (except in rare cases.  And yes, squaring the bottom of a hole is one of them, because the end mill doesn't have to cut the center of the hole). 

Whereas a drill in a mill makes a lot of sense.  Of course you are just drilling holes, but the mill gives you unbelievable ability to position the work precisely (especially with multiple holes that need to have a relationship with each other!) that you just don't have on a drill press.  You can also use the mill's auto-feed to maintain feeds correctly, and it typically has better control of speeds as well.