You can grey out the cell by using a simple formula rule, =A1<>"" applied to any cell will apply the rule when A1 contains data, this can be applied anywhere it is needed.
Conditional formatting will not disable the cell, it will only change the colour. People will still be able to change what is in the cell, if you want to stop them from changing the cell altogether then you will need to use data validation, for that the rule would be =A1=""
Note that you can use both on the same cell in order to disable entry and grey out. Anything that was already in the cell before the rule was enforced would remain hidden in the cell, to delete it would require vba.