WRT to the first part of your question, the answer is yes. The parameters of the Fourier transform can be set via sympref
This result looks a bit funny, but you can show it's equivalent to the expeted result
simplify(ans - (dirac(f - a/2/sym(pi)) - dirac(f + a/2/sym(pi)))/2i)
Check the bottom of the doc page for fourier() to see how it's parameterized, and then the doc page for sympref to see how to set the parameters and how to use sympref() properly within and across Matlab sessions.
As the second part of your qeustion, the doc page for sinc says: "Although sinc appears in tables of Fourier transforms, fourier does not return sinc in output." Trying to get an expression rewritten in terms of sinc() seems to be pretty hard.