I used to pick up microwave ovens from the trash and fix them by swapping parts. The answer is definitely no. They have very high voltage ratings, but for the safety of anyone servicing the oven almost all come with a bleeder resistor (internal or external) so they are safe to handle after 30 seconds of unplugging the oven.
They also have no real storage capacity. Their purpose is to raise the voltage on the magnetron start circuit to about 4k volts. Once the magnetron begins conducting the transformer acts as a choke on current.