Non Plated Through Holes in Eagle
Yes, in eagle "help hole" (I'm a eagle CLI nerd)

HOLE

Function 
Add drill hole to a board or package. 

Syntax

HOLE drill •.. 

See also VIA, PAD, CHANGE

This command is used to define e.g. mounting holes (has no electrical connection between the different layers) in a board or in a package. The parameter drill defines the diameter of the hole in the actual unit. It may be up to 0.51602 inch (13.1 mm). 

Or if you like clicky buttons:


Will board houses be able to do this?
Yes -- it is not uncommon. I can not speak for how they accomplish this in processing, since some boards are drilled before etching + through hole plating, but check with your board house before ordering.