It's doable, though you'll get a lot less overlap in classes than a CompE or EE would. I know a number of people that have done CS as a minor with their MSE degree, and they seemed perfectly happy with that.
What do you want to do with CS to have it compliment your MSE degree (or vice versa)? Often you can just take a minor and manage to take all the classes you're interested in and get to skip all of the boring required classes for the major. For example, I did a minor in physics so I could bypass the physics track for lower level classes, their higher level E&M stuff, and a bunch of other boring classes. Instead, I just got to take quantum mechanics, thermodynamics, and solid state physics; all of which were classes that tied in closely to my MSE degree.