I can see no reason for the unit would not work with the motors removed, but the motors are used to calibrate the unit whenever it is plugged in. This should be no reason why you could not calibrate it once the unit has finished its start up process.
In the end you have nothing to lose, You can always buy another one at a worst case scenario.
To ensure that you get the correct Grease, a decent RC shop able to supply the correct stuff for you.
If you are replacing one motor it will be just as easy to replace the other one when everything is removed.