Should be OK. The cable from the dish to the power inserter should really be SCC (solid copper core) and that should be possible, won't affect the cabling in the house. But even if the cable from the PI to the dish is CCS, should not be a problem unless the cable run is very long.
Because the frequency band used by the genie-to-client interface is much lower than regular DirecTV, even RG59 will work OK unless the cable runs are VERY long. RG6 CCS isn't a problem, in fact the signal losses in CCS and SCC are EXACTLY the same. SCC is recommended for the run to the dish because it carries power to the LNB at the dish, and the voltage losses are somewhat less in SCC than in CCS.