I'll first say that that is a very specific scenario, and one that hasn't any equivalent in any of the canon or post-canon material that we can draw for (as of now), so I don't think there is any wrong way of doing i, and thus, I'd recommend going with whatever fits your story better.

That said, as for my interpretation of such a scenario:

As it's been pointed out above, Sburb influences the reality of its players since conception, as they, and their ancestors, are literally conceived within a session in most instances. Of course, there are exceptions, such as the Beforus trolls not being able to be born in the Ectobiology lab, and thus scratching their session, and then being made by Karkat in the Alternian trolls' game; or how the Alpha Kids had already been made by John in the Beta Kids' session, thus making Ectobiology redundant.

This is not to say, however, that everything is predetermine in Sburb. The Kids' and Trolls' session were uniquely messed up due to their connection to Lord English, and as those are the sessions we follow in Homestuck, some have the tendency to think doomed timelines are a feature of every game. And they might be, considering its reliance on self-fulfilling paradoxes, but I would argue, not as much as the ~4 sessions we see play out in Homestuck.

This is all to say, I think it is absolutely possible for a player from another session to become a proper player in another one (as opposed to what we see in Homestuck, where players enter other sessions, but the sessions themselves still fill very separate from each other, if that makes sense). How that would play out, however... Well, there are a few scenarios I would consider exploring.

First, consider the player's classpect: a Muse of Void. One of the most powerful classes, one who inspires Void, so, secrets, obfuscation, the occult, the Furthest Ring, and endless potential. This to me actually makes a lot of sense to a guide type player. How Sburb would react to their presence is, again, up to your own creativity, but with that was presented, I would probably go with a sort of. New Game+ approach. The session was scratched after all.

Hope this wasn't too big a wall of text I also just woke up I so hope it isn't all gibberish lol