Hi @3dprintedrov, welcome to the forum 
That’s not a board type we’ve tested or actively support, but if it runs ArduPilot firmware then it’s at least possible it may be able to run ArduSub (although even if it runs it may not support all functionality).
The ArduPilot firmware builds do seem to include F405 options, so it should at least be possible to flash on an ArduSub image without needing to build the firmware yourself. From there you’ll need to do tests to determine which features are available, and you may need to make custom firmware builds if code modifications are required to fix/enable non-functioning features that you want to use.
The Pixhawk 4 works (mostly) when running the development firmware, and
we’re about to release our own flight controller, but neither of those options is in the <$100 range like the one you linked to.