Not necessarily. ISRO needs NASA's Deep Space Network to communicate with spacecraft only when it gets too far away from Earth. ISRO's Bangalore DSN can handle it during initial days (how many?) of launch.

Moreover, NASA is launching MAVEN (Mars Atmosphere and Volatile Evolution) in November. So, it looks like NASA's DSN will indeed be operational despite govt. shutdown. Let's hope for the best.

http://www.thehindu.com/sci-tech/science/indias-october-28-m...

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Update:

"NASA/JPL authorities have reaffirmed support for the MOM as planned and stated that the current US government partial shutdown will not affect the schedule of MOM," Bangalore-headquartered Indian Space Research Organisation (ISRO) said in a statement."

http://indiatoday.intoday.in/story/nasa-reaffirms-support-to...