Ethical Hacking

Yes, you can do both the things simultaneously, there is no issue.

MBA IT is to prepare students for business development roles in IT companies not for technical roles. To be an ethical hacker, you require strong system programing skills. If CEH provides you strong skills, then even without MBA, you can be an ethical hacker.

Ethical hacking means hacking something without breaking any rule or doing hacking for good purpose, and not stealing data from someone.
For cyber security, you should have the knowledge of hacking, so that you can stop a hacker from doing bad things. You need to find the digital footprint of the hackers to stop and catch them.

If you want to be ethical hacker then you can join DRDO.
If you won't than there are some requirement in Intelligence Buero department for the computer specialist and they will train you for ethical hacking.
Also, police hires computer specialist for IT forensic cell.
If you want to pursue some course then I would suggest you to visit website of Forensic University, Gandhinagar.
This university is Gov. University and also trains police officer for forensic cell.

Well, you can start with anyone, either of Ethical Hacking or CCNA, since they are different areas but I personally would advise you to know basic networking at least before you go for EH or CCNA.
EH has a very good exposure presently and high demand in job market rather than CCNA.

There is a lots of chance for white hacker. Cyber security is the most booming area nowadays. So, it is a better opportunity to start career. You can work as VAPT, participate in bug bounty, do CEH of entry level to pass for all. Side by side, you can complete your Master's degree.

In Pune, Arizona Infotech is a good institute for Security course like CEH, CHFI, ECSA, etc. There is no need but doing it is always better.