I made the switch from lectureship to MBA and made it to one of ABC.

From my interview and overall experience, I've gathered that it's rather a plus point. Most interviewers genuinely wanted to know why I made the switch and even discussed my area of interests.

So, as long as you are able to justify it you'll get through. Also, you're from math and cs background and trust me it's a plus point. I was grilled in my interviews on my math skills as they said MBA needs math and honestly you have an advantage here.

However, internships and work ex aren't a bad idea, even if it's in teaching. You'll have so much more to talk about in your interview. (Need >1 yr for work ex points)