The coax from the Tailgater must connect directly to the Dish satellite receiver box. Now to qualify that a little. It can go thru the RV internal coax wiring as long as it does not go thru any intermediate devices such as the antenna switch box or amplifier. So the answer is probably not unless you can redirect the internal coax directly to the sat box. And you do have to have a Dish 211 type sat receiver box. You can't just connect directly to the TV.
On some RVs there is a dual coax connector wall plate with a short coax jumper between the two, maybe near/behind the TV. You may be able to remove the jumper and connect a coax from the incoming coax to the sat box. That is how mine was wired before I added a new external coax connector specifically for the Tailgater.