Post MBA Consulting without prior experience?

I'm currently a year out of undergrad working in FP&A for a mid size company. I originally wanted to get into FP&A for the exposure and opportunity to work with upper management, along with being able to understand exactly how the company and industry works.

It gave me the exposure I wanted, and touched on learning more about how the company and industry works (mainly determining key drivers) but the monotony of the work is something I don't enjoy. Every month the same reports are due at the same time, and the same calls / meetings scheduled for the same day, among other things.

I've been looking into consulting post MBA due to the ability to travel, get a more in depth understanding of companies and industries, and solving problems (opposed to updating dates in models every month and being done with it).

Anyway, is consulting post MBA without prior experience possible? Assuming I get into a top MBA program in 2-3 years.

Edit: I'd also like to relocate to a smaller and lower cost of living city in the future (think Houston/Raleigh) if anyone can shed light on the offices in locations like that.