Hello,

Yes you should certainly have a business plan just to get the other parts of your business model working right, and to organize your own ideas. The important things to get right will be how you will market the app and get a large volume of downloads.

I actually made a video on how to write a business plan for a mobile app which may be very pertinent to your question:
https://www.youtube.com/watch?v=EV_TWcrar0c

Because mobile apps are innovative, many things are unknown (not just monetization) so it is more difficult to plan than traditional businesses. Nevertheless, you have to get 3 parts very right:

1) Building a product that will be competitive within the niche you choose
2) Eventual monetization
3) How you will get hundreds of thousands or millions of downloads (yes that many!)

I hope that was helpful. Is that the kind of an answer you were looking for?

Best,
Alex