I have never seen an individual with an infection suffer blood loss as a result of the infection, but it is true that they may not recover from blood loss at the time of the initial wound which created the infection, or that they could be infected by a forgotten beast/titan/other syndrome that causes constant blood loss and rot (which creates an infection until surgically removed by a doctor.)
As far as I know, they do absolutely nothing until some point in the future where that individual keels over on the spot, having "died of infection." I couldn't even tell you what the time frame usually is or how it is determined, and the wiki doesn't have any information either. It could be a random daily chance as with the artifacts; "today you have x% chance to die, roll to save!" where x is an integer which may or may not actually change. I've seen dwarves in fortress mode recover from an infection after some time, or the infection cleaned by a doctor successfully while still in the hospital, but the majority will die. Sometimes it takes years, sometimes under a season, and usually you have no idea they developed an infected wound during their last encounter, they just flop dead before your eyes with no status changes.
Good luck getting your adventurer to live long enough for the infection to kill him, I just usually ignore them because some groundhog rips my throat out instead.
However, continue your experiments and report your findings.