I've been thinking abt this for a while but when JD didn't know he had a son he obviously wasn't in a good mindset at the time. What would have happened if he choose to give up? If Doc hadn't showed up or if him and Rhonda split. If he felt like he had nothing to live for anymore.
He was pretty close to drinking himself to the afterlife
Boy oh boy! Someone asking about my fics!
So, if Doc hadn't shown up when he did, then JD would have drunk himself to death. Even if some hikers had found him at that specific time or Rhonda had managed to drag him to somewhere for help, without that postcard, he would still be convinced that all of his brothers died without him.
Though I guess if Doc didn't get him that postcard, someone else would have gotten it to him later. Imagine being Bruce, sending a blank postcard to your estranged brother because you just want to feel like you're sending SOMETHING to one of your brothers for your wedding and he's the only one you have an idea of where he is. And then some time later, the mailtroll comes back and either says your brother is dead or in the mental hospital.