Any post college, professional work experience will count for b-school admissions purposes. Everything you will need for your Master's you will get in your chosen program. you will, of course, be wise to indicate how your work experience has prepared you to lead and to do well in your desired curriculum, including how it will tie into your short and long term vision.

Hey aman,

First up, since you have provided only a gyst of your qualifications, it's hard to comment on the likelihood of getting into the HEC Paris or the LBS MiM programs. Having said that, your academics and GMAT seem solid and yes, your stage acting will be counted as work experience.
Most of these schools look for diversity in culture and academic background for their programs and your profile is most likely to be a unique proposition for the school.
Other factors that the schools will take into consideration are international experience, LORs and Essay questions. So, it is very important to nail these portions to stand a good chance.
As far as LORs go, LBS looks for a professional recommender and an academic recommender. HEC ideally wants two academic recommenders, but one professional recommendation is allowed. So make sure that you're in touch with your faculty from college or any other intensive coursework completed.
In your essay questions, make sure to elaborate on your experiences and how the program will help further your goals in life.
You can get a better idea about the two programs in the following links:
HEC Paris - https://www.mim-essay.com/hec-paris-mim-review.html
LBS MiM - https://www.mim-essay.com/lbs-mim-review.html

I made it to HEC Paris too. This is for many on this forum who're looking at suggestions on how to go about putting in the best application. When I started off, there were a lot of things that I wanted to put in my application. I knew I needed help of consultants who could help me prioritize as well as structure my content well. I took the services of Gyanone (India) with this and was really happy with the outcome. They helped me highlight all the relevant aspects of my profile very well. I'd recommend them to all MiM applicants.