Yes, I am referring to the metal part of the casing on the serial port, which is the part you'd be most likely to touch by accident I guess.
How do I know it is grounded? Well, only because it is common practice to connect the metal part of the casing to 0V. It's not connected to "earth", but it's usually connected to the 0V rail on the secondary side of the power supply, which most components use as their "ground" reference. The connection to 0V on these connectors is for screening purposes mainly (to reduce interference & noise), not for ESD protection or anything like that. But, if you were to accidentally discharge a static build up onto the 0V supply rail via the metal part of the connector then this would be a lot less likely to cause damage to the machine than if you were to discharge via one of the I/O pins.
As I say, if you're paranoid about zapping your machine (like I am) either wear an anti-static wrist strap (safest option) or, for a little peace of mind, earth yourself by touching an earthed piece of equipment before handling the machine. A radiator is my favourite.
I feel compelled to add that you should never ever follow this advice whilst poking around inside the cover of a dangerous piece of equipment where high voltages are involved. If you're working on dangerous, live equipment (in which case you should be a qualified Electronics Engineer) then you generally should not earth yourself at all, and certainly not via your other hand because if you earth yourself with one hand and take a shock with the other it can be game over as the electric current takes a path through your arm, through your heart (stopping it in the process) and then out through your other arm!
Of course, there is no such danger involved when handling an Amiga computer so it can be a good idea to just tap a radiator or something like that before you muck about with the machine so that you know you've discharged any static build up from your body.
Apple Hammer