How we handle kids in relationships always seems to be a contentious issue, and what works for some doesn't fit with others. As parents of course we're the ones with the responsibility for the kids, so I'll offer up a suggestion or two, but of course it's your call.
It's admirable that Randy and yourself are taking a look at stability, and acknowledging that your relationship for whatever reason may not provide that for your kid.
That said, they're not china dolls, and cannot be protected from everything. Life involves a number of people coming into and out of our lives, and our health depends on being able to forge new relationships and deal with losses along the line. It's certainly problematic if people are passing through their lives randomly and repeatedly, but it doesn't sound like anyone involved here is intending on irresponsibly jerking around your son.
The biggest indicator here I think is that your son is looking for answers...and a relationship. Those who are important to you are likely to be important to him. There's an advantage here that your son should be old enough to reason with him about what's going on with Randy, and what risks there may be in how much time there may be available, and the risks involved in getting close to someone who may not be around. Your son has an opportunity with Randy that most kids don't get very often, the chance to go into a relationship with his eyes open. It's no guarantee that there won't still be tears and heartache down the line, as in any venture...but at least it will minimize the disappointment that frequently accompanies the breakup of relationships that were supposed to be "forever and always".
Your son is looking for answers, and you have enough of the questions to help him on the journey. As long as you're honest with him, and yourself, you can't go too far wrong.
Welcome to the Forum.