First, a correction: 24VAC to 5VDC would be called a step down converter, not a boost converter. A boost converter generally means bumping voltage up and not down.
The short answer to your question is that yes you can connect the expansion board to an arduino. The expansion board consists of the following pins:
– one VCC (3.3V)
– two ground pins
– shift register OE (output enable), DATA, CLK, LATCH
– expansion board sensing pin
The expansion board sensing pin is optional, you don’t need to connect it. The other pins need to be connected: one GPIO for each of the shift register pins.
To connect 24VAC adapter, here is what you should do: connect one wire of 24VAC to ground (share ground), the other to the solenoids’ COMMON (COM) wire. You don’t need a 24VAC to 5VDC converter, if you don’t mind using a separate USB adapter to power your Arduino. The reason OpenSprinkler uses 24VAC to 5VDC converter is to allow a single power supply design. An alternative is to use two separate power supplies: one USB to power Arduino, one 24VAC to power solenoids.