Re: 150 hp Mercury Ourboard
Drop the lower unit, see if the vertical shaft has broken. If not obviously broken, turn the shaft to see if the prop shaft turns, if not then disassemble for inspection.
I would not fire the motor and wait for the stat to open to see a P stream, I might pull a stat, leave the cover off and see if water comes out within a few seconds of firing the motor, but I wouldn't run it more than 15 seconds or so.