Motorised devices and motors make noise. The specific noise any motor makes may or may not be objectionable to any particular individual, based on frequency and volume. The fan and resultant air motion will add to it. What bothers one may not be a worry to another, so take input accordingly. If your 4.5R insulation will be on your ceiling, not attached to the roofing/sarking it should dampen the noise.
Basic solar fans run when the sun shines. They generally have options (priced) to add thermostatic controls but looking at the documentation from Bradford it appears yours does not have that as an optional package, but adding one should not be difficult and could solve your problem.
If you have or are about to install a PV system you don’t need a solar powered fan since your PV system will run it, you just need to have a power point added for the fan.
Whether or not you go with another solar powered unit be sure your quotes include a thermostatic control so it only runs when the ceiling cavity gets hot, and an on/off switch remote to the fan placed so you can reach it.
In your place I would first install the insulation and assess the noise. If the noise was treated I would investigate adding a thermostat ; the insertion of an on/off switch and thermostat should be easy even if Bradford does not reference them as options or provide a kit.
For piece of mind you might contact Bradford to ask, and I presume adding them affects your warranty, another issue.
Some homes have exhaust fans/vents that push air (humidity if from a bathroom, or smells from a kitchen or toilet) into the ceiling cavity so consider what might be circulating in the ceiling; others have ductwork to the outside. Whether that matters in your case? If it does you may be better placed for a fan (or whirlybird) to run all year to avoid damp in winter, potential mould, or less likely odours, even when it seems contrary to good heating/cooling practices.