Obviously, puberty is the process that allows teens/men to get 'boners' from sexual arousal, and Jazz didn't have anything like a normal male puberty, so I wouldn't expect he could get an erection - probably not on blockers, almost certainly not once he was on female hormones. But... when you have a baby boy, everyone warns you "don't get freaked out when your newborn has an obvious stiffy. It's normal - you take the diaper off, they're, well, 'stimulated' by the fresh air, and you get baby boners." Even knowing to expect them, it still just felt odd every time it happened... you don't really get used to the sight of a tiny baby with an obvious erection!
I'm sure I've read more than once that testosterone levels are actually super-high in newborn boys (so baby erections are still likely the result of male hormones), but then they drop again until puberty... so Jazz has almost certainly had an erection or a whole bunch of them, even if only when he was just a baby.
Of course, there are other reasons his leftover 'erectile tissue' could swell/become 'engorged' besides hormones/sexual arousal... anything that causes increased blood flow to that area (maybe triggered by the healing process, or his immune system's response to what it perceives as a serious injury) could be the reason it's now swelling up. Hell, the 'injury' in itself could have directly caused the swelling... I know I keep going back to childbirth, but you're swollen down there for weeks post-baby, swelling is a perfectly natural response to 'trauma' in many (most?) parts of the body.
Basically: I would assume his remaining erectile tissue is "engorged" because his body is responding as if he's had a major injury... which let's face it, is a polite way to describe the horrors this poor kid has been through... that or he's bleeding internally and has a clot or a hematoma down there, all possibilities which are not horrific at all (/sneed)
My question is, why does he have 'leftover' erectile tissue at all? I know they didn't have much to work with for his surgery, but you'd assume if this is not an uncommon cause for complications post-SRS (which seems likely, given several Kiwis already have chimed in with evidence of the same thing happening to other troons) they'd be cautious about keeping too much of it... what would he ever need it for?