I'm quite successful at it with only a Mathematics degree. However, I started at my job about 11 years ago and so things could have changed a little, but I doubt it.
Looking at...
http://en.wikipedia.org/wiki/Project_controller
"'Industry experience' is often a pre-requisite and so controllers often have undergraduate degrees in related fields. Also, many analysts originally enter this domain through their practice as consultants or accountants and so a very wide range of qualifications is common."
Project controls is VERY niche-dependent. The skills I use for scheduling are universally-applicable, but when I then apply that scheduling with respect to a change order I need to be able to know construction means and methods as well as have an idea of what the real nature of the work is in practice in the field. I'd hire X with five years construction field experience before I hire Y with ten+ years financial experience, even at the same compensation package.
I do construction project controlling and have never worked with nor would really consider hiring an accountant over an engineer. Accounting would be useful and would pretty much ensure that they'd be able to handle the analysis part of the job, but so can an engineer. Field experience is worth a lot more than the degree, period, and an engineer at least as some grounding in construction that can be built off of. I have a basic understanding of every system in a building (mech-elec-plumbing-comm-finishes-structure-civil) because I need them, and the only real way to get them is with practice and exposure, and that's something that an accountant just isn't going to have access to.
Professional certification with an MBA or MSF wouldn't be useful in construction, but I imagine there's plenty of project controllers that could get work with those... just not in my portion of the industry. Even as it is I don't really consider ASCE or PMI accreditation to me of much merit (as I generally work in the field rather than as a claims consultant where you'd really want to have those letters), just like I don't consider MBAs to be all that useful in general.
They certainly seem to get the executives all hot and bothered, though; as a longer-term plan it'd probably be worth it but getting your foot in the door wouldn't need it.
Plus, in tech and financial fields you're less valued. Construction as an industry doesn't generally attract lots of number-crunchers and analyzers and proficient writers and negotiators all rolled up into one package, and I benefit from it. Its the difference between being the IT maintenance guy at an accounting firm or the IT maintenance guy at an IT firm.