RF on outside of coax

 Without going into too much detail it is accurate to say that current flows out of the center conductor of the coax and the same exact amount of current, in the ideal conditions, will flow back to the source and should be inside the coax or on the inside of the shield. Essentially the shield can be viewed as two conductors or wires. When the current starts to flow it has a choice to return to the source over either the inside wire or the outside wire. That is inside the coax shield or outside the coax shield. The factor that determines where the current will flow depends on the ratio of impedances looking down both paths from the antenna connection. If the outside path has a high impedance relative to the inside path then no current or an insignificant amount of current will flow on the outside of the coax. The length of the coax becomes extremely important here as the impedance varies from high to low as the length of the coax is varied. If the impedance is low looking down the coax then simply changing the length of the coax by 1/4 wavelength ( shorter or longer ) will make the impedance high. For example a wire or length of coax that is open at one end and is 1/4 wave long will have a low impedance at the other end. A wire or length of coax that has a low impedance at one end and is 1/4 wave long will have a high impedance at the other end. In general the RF voltage at the center of a dipole is low. 

The outside of the coax can be thought of as a wire. In the simplest of cases it may be grounded at the transmitter end to it may be open. In reality it is probably somewhere in between. When my first transmitter was hot with RF I learned very quickly how to fix that with an open wire connected to the chassis of the transmitter to move that hot spot down the wire to the end. I also quickly learned not to touch the end of that wire when transmitting! 

The current on the outside of the coax will radiate a signal. If all the return current was inside the coax we would have equal and opposite currents and that would cancel the radiation from the transmission line. This radiation may actually be good for a general purpose antenna, however if the antenna is a highly directional Yagi it will probably distort the unidirectional pattern and reduce the front to back ratio.again that may or may not be a problem. I am skeptical that a balun will have any noticeable effect on a dipole.