I'm fairly new to the GIS world, and have a quick question. I'm currently using ArcGIS 10.1. I do not know much about rasters, so does transforming a DEM from one projection to another automatically convert the units of the cell elevations?
To expand a little on Ryan's answer, a raster DEM is just like many other rasters, it contains a numeric value for each cell. That value could be elevation in feet, temperature in degrees C, or anything else that can be represented numerically. Reprojecting it to another coordinate system would not change the values in the raster cells, because GIS doesn't "know" that it's an elevation value that should be changed (unless you tell it).
Also, horizontal and vertical coordinate systems are two different things, just because your raster is in UTM Zone 17 North, NAD83, Meters (or whatever), doesn't mean it will have elevation units in meters as well, or even that it will have elevation values at all.
No this should not change with a projection.
The numeric value of the cell is the Dn (digital number) which generally is represented as units above sea level.
You need to know what the original data was created in (ie: feet, meters, etc).
With that information you could convert to another format and transform the z factor also.