It depends on what you want to do. At the graduate level, many electrical engineers in signal processing, communications and control have taken some functional analysis course, and courses based on A.V. Balakrishan's Applied Functional Analysis/ Luenberger's Optimization by Vector Space Methods or similar are pretty common as well as courses based on Naylor & Sell's Linear Operator Theory in Engineering and Science and a lesser extent Young's An Introduction to Hilbert Space (I have been told that undergraduates in EE at Rice use this for a bit - it is really an undergrad book). At some point though, the line between "mathematician" and "engineer" does get blurred. Its a useful course thing to know in some cases if you're an engineer whose doing research heavy in probability or control theory, especially.
That being said, those books differ considerably from whats typically offered in a math department (usually start with something like Rudin's Functional Analysis or Conway's A Course In Functional Analysis). In math department courses, you are dealing with operators to study properties of Hilbert/Banach spaces. In contrast, in engineering, we typically have the properties of the vector spaces (usually something nice like $L^p$) and want to study the properties of operators (such as minimizing some functional or something).
All in all though, for most people, if they have to ask the question, I'd say they should probably be looking for something else to take, especially if they tend to the more applied side of things.