No, you need to buy a 24v C adapter transformer. The included adapter will not give you a 24v supply from a high voltage source, it is for traditional furnaces that have an accessible 24V transformer in them. Your transformer is soldered to the aquastat, and the 24V voltage terminals are not directly accessible.
I’m assuming you only have 2 wires in your run to your current thermostat? You need to power the wyze from a 24VAC C adapter that is plugged in near the thermostat. unless you are able to run more wires.
Example of the proper type of adapter: https://www.amazon.com/dp/B07L4DN5R2
Unfortunately, with 2 wires, you will have to plug that adapter in somewhere near your wyze and run the wire up the wall to it. Connect the adapter’s wires to Rc and C and the red and white wires that run to your boiler to the Rh and W1 wires. Tell the wyze in the app that you have Rc, C, Rh, and W1 wires and it should work with your system.