Can you really put 2 transformers in parallel connected to a single voltage 220VAC 60hz?
Yes, you can connect transformer primaries in parallel - after all, EVERYTHING you connect to your house wiring is connected in parallel.
Incidently, the switch in your schematic is wired incorrectly - exchange terminals 2 and 3. As shown, the switch will have no effect, and the circuit will not get any power.