Everything else boils down to "why do it?"/"Is it worth it?".
What are the advantages and reasons someone WOULD do both?
1. It is convenient, initially
Because nothing is changing, there's no need to think about how things should or would. It just stays the same.
2. It is convenient, story-wise, when complete with hosting
You don't need to explain how your character regroups, becomes more active(if you kept up the roleplay), or otherwise retransitions to a classic player role. They never left.
What are the advantages and reasons someone WOULDN'T do both?
1. It's an opportunity
Playing an RPG, and playing an RPG and hosting an RPG at the same time is a different experience.
When you play your character you are trying to bring it to life as best you can. When you host an RPG you're trying to bring the story and setting to life as best you can.
If you try to do both you're either going to put a strain on yourself, invest more time and have slower updates, or simply do one or the other or both less successfully.
However you could do the easy thing and just have them disappear for one of several easy to understand reasons, allowing you to focus on the storytelling and having them return after...
Or, if you want a challenge, you can put all your resources to into the storytelling and setting by having the character become a part of it in some way.
2. Cohesion
Despite the character going away or becoming a part of the story being different than what they were doing while they were your player when you were not hosting,
You return to him having never done double duty with them, never having to cram that down them. Your experience returning to the player role feels like a proper return and it appears that way to everyone else.
Otherwise it seems like something happened but there's no story about it it's just is kind of an odd thing that happened that we pretend didn't happen.
Either you will notice that things have changed because now you're not doing two things, or others will notice and how the character acts either way or if both, if something noticeably did change then there's no worries. Nothing to hide, nothing to ignore.
It's challenging creatively, it's easier in practice.
Edit: I would still recommend doing this, even for someone who is going to host a short chapter. So much so to where I'd prescribed the first question they ask is "So what's going on with my character throughout this?"