Will it have time/fuel to "duck and cover" by getting to the far side of the planet before the close approach of the comet and the potential of a cometary dust storm that could wreck it?
While this is a non-zero probability event, it is a low probability event. I doubt that the mission planners are particularly worried about it.
Maybe if there's a mission-compatible way of sequencing things that will reduce this low probability even further, at little cost (which is what Hubble did during a predicted Leonid meteor shower ; but the Hubble Deep Field South was already planned, and the only real change was when the exposures were scheduled. Which by coincidence pointed the HST away from the radiant of the meteor shower.)
Incidentally I note that the mission is being monitored by the Indian Deep Space Network. Which either operates for a few hours a day (per mission, depending on direction to the spacecraft), or indicates that India has done some significant multi-national diplomacy to get their ground stations into a number of countries.
LMGTFY. There's a Wiki page that says it's one site near Bangalore. And that mentions the use of steerable antennae to " improve[s] the visibility duration". But this site says there are a number of other tracking sites. "ISRO Telemetry, Tracking and Command Network (ISTRAC) [...] has a network of ground stations at Bangalore, Lucknow, Sriharikota, Port Blair and Thiruvananthapuram in India besides stations at Mauritius, Bearslake (Russia), Brunei and Biak (Indonesia). " So, maybe several different organisations, with overlapping missions and facilities. Like Topsy, it's probably something that "just growed".