Will having a minor increase chances of successful music industry career?

Finance, accounting, bookeeping, patent law, digital rights management, personel management and classical piano, depending on what's available at your school. Music is subjective science and objective aesthetics. The first four bars of a tune capture or lose the listener. Personalities drive the industry. Great singers often regret turning down songs that their rivals turn into hits. Foreigner let record execs hear songs under a false name; the execs said no. When the songs were released under the proper credentials, they went platinum, the execs went out the door. There are metrics, there are 'formulas', there are middle-men, and sub-contractors (arrangers, backing singers, copyists, mastering engineers, roadies) to pay or pay attention to. Finance ALWAYS figures in ways artists don't understand. First, verbal agreements are only that. Second, in a complex contract, read the 'riders' (small print). Enthusiasm needs to be backed-up with diligence. Money is the root of all conflict, or reward of precise planning. Get your friends to help. Love the craft.

I have a strong opinion about a business background when music is your major. Marvin Turen hit some great points about music business.
I know many musicians with and without degrees in music. Most of those who are successful are great at managing time, money their products and have great interpersonal skills.

It depends on the minor. If you are majoring in music, consider what might complement your experience for greater success. Perhaps a minor in business, music technology or even computer programming could help round out your skills. Look at your future career goals, read some job listings and note what skills are being asked for today.

Hi. I have no idea what your minor would be, so I can't answer your question fully. But more education can never hurt and only help! If you have the time and energy in addition to your major field of study, then go for it - take a minor, too. All the best!