yes you can use the factory antenna. it may require removing the plastic connector end that surrounds the sat antenna. to do this there is a white insert that must be slid out of the sat radio antenna connector end then the entire plastic housing around the connector can be unclipped off the metal cylinder sat radio connector.
second, that jvc adapter you are looking at is a sirius interface. what exact model jvc unit are you looking at? if the jvc says "siriusxm ready" then you need a (sxm v200) module available at most car audio shops. if it says "sat radio ready" or "sirius radio ready" or "xm radio ready" then you can use the adapter you listed from crutchfield.
let me know which exact radio you're looking at and i can point you in the right direction. the connector i'm talking about is below... this is not a jeep/chrysler exact part, but it looks almost identical... you can remove the white insert on the side then you can remove the entire yellow housing. the remaining round silver connector plugs directly into the V200 satellite module.... just carefully mount the v200 box to avoid damaging the antenna connector and you're good to go.
link to crutchfield with v200 adapter