The simple answer is that you can connect a solid copper wire between the center post of the generator and the ignition coil. However, it will be necessary to take a separate wire and insure that a clean ground point on the generator, such as the tab on the outer coax casing, is connected to the negative or ground terminal of the ignition coil circuit. If you do not have a ground wire between the two components, your circuit will not be complete, and the function generator will not generate a signal.
The advantage of using a coaxial cable to connect the generator to the ignition coil is that higher frequencies will be transmitted more effectively. The significance of higher frequencies results from the fact that square waves ... or switching waveforms ... have sharper edges that are composed of the higher frequencies.
Coaxial cable is designed to transmit relatively higher frequency signals with as little attenuation as possible.
If you have access to an oscilloscope, you might try to compare the sharpness of a square wave, observed at the function generator output, with the sharpness or attenuation of the square wave measured at the ignition coil, after it has traveled some distance to the coil.