I recently heard that remark "piss hardon" from a 15 year-old. It was never in my teenage lexicon back in the 1980s. I was flabbergasted and deeply suspicious about where the term came from... To me it is BS. I'll explain:
An erection from a full bladder? Doesn't make much sense. The sex drive and your urge to pee are two different things (not counting those who are turned on by "water sports"). I have had morning wood whether I wanted to pee first thing in the morning or not; and the morning piss does not normally reduce my sex drive either (although, if erect, I need to calm down a tad to pee comfortably). Sometimes after a morning piss I get aroused again right away, 'cause my mind is lost in raunchy thoughts, and then it's time for some play! ;) My personal experience, and interaction with other guys, taught me that separation - I've had no experience to prove any connection (btw: no bf ever observed this "piss hardon" idea with me).
I suspect the "piss hardon" is an idea/term that may stem from confusion about male anatomy combined with, for some, a feeling of shame about being aroused - a term to excuse the erection invented to deflect the truth for those who cannot handle the fact that we are sexual creatures, and that men get erections. Empty-the-bladder-and-that-evil-erection-will-go-away... Gee, I wonder what cultural mindset of the last century has that kind of thinking? All boys schools? The military culture? Religious right and their education "system"? Hmmm... Well my "evil" erection doesn't always go away, so there... lol
Bottom line in this case: for me there is no connection of consequence - only coincidence and circumstance - and maybe something psychological.
rksportwear is correct about us getting erections all night - the coincidence is our bladder filling up too. The term "piss hardon" suggests a causation but really its two different body functions affecting the male reproductive system at the same time. I have never noticed any connection with morning erections and a need to pee - they have always been separate but coincidental things to me and I know my dick really well ;-) (Jerk-off, then pee or pee then jerk-off, or sometimes just pee cause I'm in no mood for sex, or even jerk-off then pee then jerk-off some more. That's why I question the whole idea!)
Sometimes nature fools us and we assume somethings are connected in ways that aren't exactly true. Mind you, it could be that some men actually have a connection, but I certainly don't and nor have the men I slept with. Which is why I believe the term is just a cultural fallacy.