Any ME program will have a good 3 or so classes minimum in EE. In today's market you have to know the basics because everything is intermeshing. It's not like you'll sit down and anylize circuit diagrams or anything like that, but there is a lot of theory and knowledge that is just plain day to day language and understanding. For example, in my area, R&D, I work closely with EE's in our data syatems and our engine control systems. I have to know how sensors are implemented and work, PLC's, and basic industrial control schemes for heaters, coolers and such. It is mandatory to know how these things operate for the inevitable breakdowns and troubleshooting of systems. It's not super high end digital stuff, but it's all in an area that is not considered pure ME. Without a basic understanding of electrical engineering, you can be at a real disadvantage depending on where you end up career wise.
Don't be afraid of braanching out and learning something new.