Only HP knows what HP has designed (and why) and as such one can't simply assume that a connector on a system is 'standards' compliant and not a 'psudo proprietary' connector (as seems to be the case with your PEG connector that is missing pin #3).
Normally a 2x3 PEG connector can supply 75W and as such, each 12V pin supplies 1/3 of this power budget. That means the HP 'psydo proprietary' PEG connector, for the want of a better term, may only be capable of supplying 50W (if each ping is kept to the same current capabilities as used in the standard 2x3 PEG connector).
This then seems to indicate the Z620 can only support a 175W graphics cards (using 75W from PCIe + 50W from each of the two 2x3 PEG connectors). Note that the standard allows 225W graphics cards pulling 75W from the PCIe slot and 75W from each 2x3 PEG connector!
So, one way to quantify this is to look at the quickspec for your Z620 and see what graphics cards are certified for use with your system. Then knowing what cards are certified for your system, you can check what PEG connectors if any are provided on these certified cards and also check what their power consumption is. I'd guess that HP has not certified any graphics cards that require more than 175W of juice...
Since you say your card draws 165W, that power budget seems OK when considering the above. So it should just be a matter of plugging in both 2x3 PEG connectors and all should be well.
However, it you want a more powerful card, purely based on the fact that a standard 2x4 PEG connector can supply 150W using three 12V pins, this would indicate that each pins can supply 50W. Assuming the pins used in a 2x3 and 2x4 PEG conector are the same, a 2x3 power connector with only two 12V pins could in theory supply 100W each. Thus you could in theory use a 275W card in the PCIe slot with your 2 psudo proprietary HP PEG connectors. BUT this is assuming something about the pins themselves and that your HP power supply is up to the task (and can actually provide the needed 275W of power).
And i'd say that if you wanted a 225W graphics card that is supported by the standards, likley it would be a simple mod to jumper 12V from one of the pins to the vacant position normally used by pin3 (12V). I'd be surprised if the HP PSU supply and PEG wiring couldn't handle the extra 50W needed. But that may be a little too much for some who value warranty.
In any case, without owning a Z620, i'd be comfortable in stating you'd have no issue with your 165W graphics card and those hybrid psudo proprietary 2x3 PEG connectors as is 
(Heck, i've had no issues with a 35W graphics card in a 25W capable PCIe slot of my Dell T610 server which only supports graphics via the inetgrated adapter)...
But really, who knows why HP used only two 12V pins in their PEG connectors, maybe they used better quality PINS and they were sufficient for the cards they chose to certify. Maybe that 2 cents saving for one less pin was enough of a driving force... Only HP knows what HP does...