Does AC Needs Grounding?

I noticed that there are only hot wires going from the cutoff box to the AC unit outside. The cutoff box was grounded but no ground wire going to the AC unit. I am going to change the power whip with the ground wire and ground the AC unit. Is it possible that since the AC is on the ground so it does not need to be grounded? Does my adding the ground wire cause a problem? Most likely all the AC systems are connected like this in my development.

With out knowing your local code, the simple and safe answer is yes. the compressor should be grounded or bonded to or thru the service disconnect switch

Are you a Home Inspector ? or are you just looking to do a project yourself and save some money ? To answer your question, I bet if you examine the wiring more carefully you will see that the 2 insulated (Hot) current carrying conductors are wrapped in a non insulated stranded wire? That is the grounding. You really should have a qualified contractor do this for you because if you need to ask the question you just did, …well you are obviously not qualified to do this safely yourself.