1) There will be a fluctuation matching the pressure fluctuation of your boiler perfectly according to physics tables for pressure/temperature of water.
2) Shots pulled with the same grouphead temp at the top and bottom of the boiler cycle will differ in about 1-2 degrees Fahrenheit although the boiler temp swing will be more like 5-10 degrees. The shot temp difference may start out further apart, but will be around 1-2 degrees.
Resulting in the notion that PID'ing is a good idea, but it wont achieve anything more than starting the shot at the top or bottom would. I think someone posted a link of a fairly common electronic pressure regulator that has a very small deadband and is much smaller in size and complexity than a PID. This would be the best bet, although there is little documentation on these forums of it.