Is it important to be enrolled while applying for jobs rather than be unemployed?
I'll answer this question from different point of views: your potential employers and yourself.
From your potential employers’ point of view, it does not matter. What matters is your immediate availability. Most companies prefer their new hires to start to work immediately. Once they make a job offer, they would like to see you in the office like today so that they can start to train you. They don't like to hear excuses like: I have some unfinished project, I am in the middle of writing a paper, I need to go to a conference next month, etc.
So, you need to indicate on somewhere such as your resume, cover letter or during the interview that you'll be immediately available. This will increase your chances to be hired. If you cannot be immediately available for some reason, you need to provide a definite time frame when you'll be able to start.
From your own point of view, you'd better keep enrolled. Job hunting can be a long shot. It can be only a few weeks if you are lucky. It can be a year or even longer if you are not lucky. Waiting for job interview and job offer can drive you crazy. You'll have things to do while you are waiting. You also can change your mind on finishing PhD if you still have some uncertainty about going to industry.
If you are absolutely sure you want to go to industry, then you should take bfoste01's idea, do internship. You can get into industry faster this way.
Good luck on job hunting. Academia will miss you!