In full EMT installations, it would be very hard to pull romex through EMT. Also, if you need to rewire or add additional wires, it would be near impossible to do without taking everything apart. It's definitely okay to do, in fact it's required to protect cable from damage.
2008 NEC - 334.15 Exposed Work says, "Cable shall be protected from physical damage where necessary by rigid metal conduit, intermediate metal conduit, electrical metallic tubing. . . ." See also Can Romex (NM-B) be run through conduit?
An option, which may be appropriate for you, is you can run regular NM-B along the wall close to the ceiling, and come down to your box with EMT. This way your cable is protected from physical damage where it's needed, but you don't need a full EMT installation. They make clamps which secure NM cable to EMT ends. You don't want to overfill your conduit, as heat build might be an issue.
In my experience wiring my house, in the end I found it was best to do a full EMT installation and run THHN though it. It is frustrating that 500 feet of White/Black/Green 12 gauge THHN is not cheaper than 500 feet of 12/2 Romex.