I believe this should work. Can you post the full GET command you are using?
I just made a quick test on Tableau 10.1 and was able to retrieve the PDF with the quick filter displayed. The instruction I used was:
tabcmd get "/views/ServiceInterruptionAnalysis/DropCallDashboard?Cell%20Names=Rumia" --filename "C:\Temp\test.pdf"
The name of the dimension I used on the quick filter is [Cell Names].
Thank you Santiago, I will check it out!!