MBA - going to investment side?

I am 27, Senior Analyst for sales/capital raising at REPE(2nd year) - will MBA at a top school open my career as an investment professional at a buy side firm?
Feeling a little pigeonholed to a sales career...

• Being in REPE already I get a lot contact from headhunters, for SWF investment professional analyst positions, but get turned down at an early stage, once they find out I am more of a client service guy or I don't really model in my current work. This has been very dissapointing.

• Long term goals - switch to the fund manager side who’s actually doing and managing investments (preferably for alternative investments)

• I started out doing sourcing/acquisitions on a real estate firm for 3 years, then moved to an REPE for client service/capital raising as a compromise for the above, as I couldn’t get an offer for the investment side.

• I feel I’m familiar with modeling, writing IC memos, etc. - I have access to them at my current firm (which was my actual motivation for joining), and reengineering models when I have time. However, I can’t say that I have formal investment experience.

Will an MBA help me go to the investment side?
Or, is there something other than this that I should look into, like try to start as an year 1 analyst at a different shop, keep improving modeling skills etc. I’m also doing the CFA.