Absolutely nothing. Almost any engineering degree is acceptable for EME.
The chance of said EME officer actually using their skills: almost zero. We have very few R&D positions available for EME types (or any type for that matter) since our old testing facility was shut down after the LSVW testing "problems." (not saying the two were related in any way, I'm just saying
)
EME officers are largely: personell administrators (at the 2Lt, Lt level. Usually Second/Third Line Rear Echelon units); and fleet administrators (at the Capt level and at First Line Units). There are some positions available that take advantage of your degree and you never know when it will come in handy (an old Platoon Commander was able to assist me with technical drawings for a rather convoluted Technical Failure Report done a few years back, but he told me they were the first time he had used his Mech Eng Degree since leaving university).
With a background in Chem Eng, there are certain Navy Trades that really like you and some Air Force trades as well. A career path leading towards the JNCBD Coy (Joint Nuclear Chemical Biological Defence Company) might be right up your alley. If you actually want to use your degree, I cannot reccomned EME.
For some info on military applications of Chemical stuff check out RMC's Chem Eng department page. http://www.rmc.ca/academic/chem/index_e.html
I know a couple of Chem Eng types, but I have no idea what trades they are. I can find out if you like. Send me a message or email with detailed questions and I can get you some info.
Wook
Arte et Marte