Modifying power strip in enclosure to attach to power entry connector
We'd like to know if this is a safe way of doing this


Yes if you can use a crimper correctly there should be no trouble.


  And if so, do we need to attach the ground to the enclosure


You should. The legality depends on your country's legislation, whether the whole thing is Class-I or Class-II but if you use a power strip with ground on it, then I will assume it is Class-I. In this case, protection earth (not "ground" in this case) must be connected to the metal enclosure, and it should not be flimsy. Usually this is done by means of a crimp terminal with a hole, a metal screw, and serrated washers.