I'll relate a few things from my experience. Maybe helpful, maybe not - I understand that we're all different creatures. But I see a little bit of myself in this passage, so here goes.
I finished undergrad in 2008, went straight from undergrad into graduate school, and got a Master's degree in 2010. Before starting graduate school, getting a PhD had never really crossed my mind - I figured I would get my Master's and then go get a real job, whatever that meant.
Halfway through the Master's, I had a cool summer internship at the Graduate School of Public Health, and was more-or-less invited to apply as a PhD student. Sure, what the heck, I don't know what I want to do yet anyway, might as well. Received my PhD in 2013, got a job and went to work.
During graduate school, one of my professors told me something that really helped me. I was remarking about how little I felt like I really understood about our field, and how I had the impression (as many of us probably do) that I was supposed to know it all when I graduated. She told me that "Graduate school is when you realize how much you DON'T know." This made me feel better; I realized that even in obtaining a very advanced degree, you're not walking away with a certification that you know EVERYTHING about that field, but a certification that you know basic principles of that field as well as HOW TO LEARN additional concepts when called upon.
Fast-forward a little bit. About eighteen months after completing my PhD, one of the cardiologists here approaches me with an offer very similar to what you've described; I am now the leader of a (small but growing) statistical group that is meant to support research in cardiology, cardiac surgery, heart transplant, and a few other niches in one of the largest hospital systems in the world. I wondered at the time, briefly, if I was actually ready to do this. It was the same feeling that I had in graduate school - Should I know more? Will they find out that I don't know EVERY SINGLE THING about statistics? Ultimately, I realized that these were silly concerns, that I knew as much (or more) about the field than anyone else they would find for the job, and that as I encountered new questions and issues, I would be able to figure them out along the way, even if it occasionally requires a Google search or two. I took the job. Eleven months in, I'm absolutely delighted. It's not easy work, but it's very fulfilling, with good people, and I feel tremendous sense of accomplishment with each new project that gets completed.
As for the last part of your post - will you have time to get to the gym, have a social life, have a relationship. Yes...if you actually let yourself do that. It is possible to be a hard worker and still have those things. There might be some late nights at the office; there might be some early mornings; there might be some times when you have to bring work home or answer emails late at night. But ultimately, if you manage your time well and do good work when you ARE in the office, you should still have time for those things. You just have to manage your time well. Most days I'm up at 5, in the gym at 6, in the shower at 7, and en route to the office by 8. Put in 10 solid hours, leave at 6, have a good dinner, enjoy some idle time in the evening. Plenty of time on weekends to travel, go do social things, or just lay on the couch and watch football.
Obviously I do not know the specifics of your position, and it's absolutely possible that your position will have a lot more work than mine. But I read enough similar-sounding stuff that I felt compelled to reply & share my experience. I vote go for it...IF this is what you think you really want to do.