Is a PhD right for you if you hate doing research in your free time but love doing it as a job?
The other answers already explain that no, you shouldn't be doing research all the time, with no time for breaks, relaxation and other interests. All this is quite correct.

However, I am a bit unsure whether the stark dichotomy "all research all the time" versus "a few hours in the morning" is really helpful here. Maybe an answer to the following question is more helpful:

Is doing a Ph.D. right for you if you plan on doing it as a 9-5 job, 40 hours per week?

And there, I would be a bit more careful. Yes, there are people who can do a Ph.D. like a "normal job", at their desk at 9am sharp and dropping their pencils at 5pm. It is possible. However, my personal impression is that these people will avoid the typical Ph.D. burnout, but they will likely not be top performers. So my answer to the modified question above is:

You will probably do fine with a 40 hour workweek, if you make sure to stay self-motivated. However, you should think deeply about just why you want to do a Ph.D... because unless you are uncommonly brilliant, you will likely not be productive enough to stay in academia and compete with people who routinely put in 50-60 hours per week. You may want to think about leaving academe with the Ph.D. and going into industry.

Note that I am not saying "40 hour Ph.D. students" are lazy. However, if you can't work up the level of passion and commitment to your topic that makes you want to put in 50-60 hours per week often, then there will likely be someone else, and that someone else will have more publications five or ten years down the road.