Depends where you want to work. If you want to get something like a 'base knowledge', you might want to consider getting your FAA ticket, though I'd recommend doing a 'proper' course (the license w/o it is nonsense - and there is schools out there that pretty much just issue that; type like get your license in a day).
I am little surprised that your mentioned crewing and mass & balance as something 'not important' to a dispatcher. Actually with smaller companies (which a more likely to give you a chance flight planning before you can start with the big one's) most of these tasks are included in the job or are sort of assistant duties to get into it. If your question refers to the issue whether a FAA license will buy you a greencard (and this is the only reason for you), forget about it.
Hope that answers some of your questions.
Cheers
fcit