SDM is a program designed mostly for experienced technology managers. The students on average tend to be significantly older and have greater work experience than even the Sloan MBA's (who aren't exactly newbies). Around 1/3 to 1/2 of SDM students are sponsored by their employers - a far higher percentage than within the Sloan MBA program (or any other program at MIT for that matter).
SDM, however, is not a direct substitute for the Sloan MBA (or any top-ranked MBA for that matter). SDM students have no direct access to the Sloan recruiting system - a feature that has generated great consternation among the SDM student body. Rather, SDM students have their own dedicated recruiting system that is heavily weighted towards technology companies. Hence, if your career goal is to enter finance or consulting, you can still do so, but the pathway will be more difficult than if you were a Sloan MBA, as you will have to leverage the general MIT career recruiting system where you will have to compete against the MIT student body writ large. Furthermore, SDM students have only limited access to the Sloan MBA course catalog, and for that reason, are largely cut off from the Sloan social networking scene, which is arguably the most important reason to attend an MBA program.
On the other hand, the SDM program can be completed in 1 year which represents significant opportunity cost savings if you know exactly what you want to achieve from the program. Furthermore, SDM students have greater access to the MIT engineering program than do the Sloan MBA's, and some SDM students are able to successfully double the SDM degree with a genuine MIT engineering master's. {To note, the SDM degree is not an MBA degree nor is it a true engineering master's, but rather it is a 'joint' - but still singular - degree in "engineering & management").
But to answer your question, it is indeed possible to double a Sloan MBA with an MS in CS (actually an SM in EECS), or any other engineering degree. The LGO program is designed specifically to do that - but be forewarned: the program is geared towards careers in operations management and requires each student to take a 6-month operations internship (in return for a fellowship), and if you do not desire an operations career, LGO will be a poor fit. You can also complete both degrees on an ad-hoc basis, which, practically speaking, requires that you be admitted to one program - probably the Sloan MBA program - and then while a Sloanie, apply for joint admission to the other program. {Interestingly, the EECS department does not admit people directly into the SM program but will admit existing MIT graduate students of other departments to complete the SM degree as a double.}
Graduate Policies and Procedures: Advanced Degrees: Master's degree 
