Yes, there is a transformer (not a solenoid) on each loudspeaker in a 70V system.
You certainly could replace the loudspeakers with higher quality devices. But chances are that the quality of the transformers, themselves, in your existing system would limit the frequency response and power handling of the new loudspeakers. Better to replace the existing loudspeakers with better devices that also have better transformers. Tannoy, EAW, JBL and a few others make very good 70V loudspeakers.
You need to also look at the power amplifier and determine whether it provides enough power and has a decent output transformer. You could replace this with a more appropriate amp that may or may not need an output transformer.
Less of a concern is the cable from amp to loudspeaker to loudspeaker. But it may be a concern and therefore needs to be evaluated.
Finally; as is the case with any type or configuration of loudspeakers, you need to provide equalization (plus high-pass filter, alignment delay and limiting) and have the system measured and optimized in order to achieve the best response.