I have been in the position, but for 2½ years, as a travelling spouse. My wife and I moved to Malaysia for her career, and I went from full-time graphic designer to part-time, then casual/freelance over about 6 months. In the end I was working maybe 10 hours per week on average which led me to pick up tennis. In our situation I was incredibly lucky to not have to work as life in Kuala Lumpur is cheap. And we have no kids.
Before moving to Malaysia, I'd literally played maybe 50 hours of tennis in my life, without any lessons/training/instruction. With my free time in Malaysia I picked up tennis "seriously", and played ~8–10 hours per week for the last 1½ years, and took 2x 2hr lessons pretty much each week for about 9 months (so cheap!)
I'm semi-fit but a bit overweight, and went from level whatever-you-are-when-you-start to current strongish 3.5 (with keeping about 6hrs per week tennis since moving to the US 6 months ago.)
End life story.
My conclusion: I can't explain how much I love the game of tennis now. It has enriched my life significantly, and I look forward to each upcoming session. I owe that all to the time I had learning and becoming obsessed with Tennis. But I went from a complete novice to ~3.25 in my sabbatical time, and I suspect that was much easier, and a much bigger and more enjoyable improvement than going from 4.0 to 5.0. In saying that, I'm still 100% hungry to improve to the next level. I'm not reaching for a specific ranking, I just want to improve myself and play challenging opponents while I'm still able (I'm 35).
So I'd say if you can afford it, and it won't hamper employment after your sabbatical, then go for it!
Caveat: In honesty, I find while getting better, my frustration level is slowly going up when I make simple errors, whereas beforehand I was still "getting the hang of it" and mistakes were fine. If I was a 4.0, I'd probably find a great deal of frustration in those six months. But that could just be me.
Racquet: Dunlop Bio Max 200G + Volkl Cyclone 17 @ 52lbs