Coiling up extra coax wil not make it like a RF choke and will not lower the signal level. As long as the coil diameter is large enough that the center conductor does not cut into the iner insulation and short to the shield, nothing on the outside of the coax will affect the strength of the signal. The signal is carried on the inside of the outer shield. Coil up all the extra you want. One thing that will affect the signal is if you have way too much coiled up (like 20 or more feet) is the extra loss in the length of coax. YOu will get the same ammount of loss if it is coiled or just ran in a line.
If you are transmitting , coiling up the coax may have a benifit as it will act as a choke and keep the transmitted rf that is coupled from the antenna from getting back to the transmitter. Discussion on this is beyond the TV application and not needed here.