Doble testing is recommended once per year for a power transformer. Its recommended to disconnect the secondary connections otherwise you'll get all the equipment up to the secondary side breaker doble tested, which may include secondary side bushing, lightning / surge arresters, secondary side insulators and even the secondary breaker. Normally it’s recommended to get all this equipment doble tested separately so that its test data could be trended and compared later.
I have never attempted to doble test everything together but it definitely should get the results skewed because every piece of equipment has a totally different Capacitance and Doble testing is all about testing Capacitance and Dissipation Factor. So if you have all the Capacitances in parallel you’d get results that are not even near the values for the transformer alone. Why is the capacitance different for the different equipment... because of the different types of insulation or rather dielectric used in the different equipment.
As regards to the HOT SPOTS... I am not sure why do you fear it would hot spots due to testing… is it due to loose connections??? Well first of all, all bolts should be torqued to the specified torque settings. Even it’s highly recommended to check the bolts torque once a year and you’ll be surprised how many loose connections you may find.
Doble Testing (Capacitance and Dissipation Factor Test) if properly conducted by properly trained personnel won’t do any harm to your equipment.