The antenna diodes are only relevant during manufacturing, when a metal line is connected on one end but not the other. ESD diodes on the other hand protect inputs against electrostatic discharge when the chip is in use.

There is a tiny amount of extra capacitance on the net because of the reverse-biased junction of the antenna diode, but that's it. These diodes do get taken into account in when determining timing though.

I thought they were there to allow Van Eck phreaking of the processor state