Power in a 110V circuit is one hot and one neutral. Neutral is also ground. The only difference is the path it takes to ground. But its ground. Which you can see if you look at the wires behind the panel. So your integrated is grounded, only just once not redundantly like it would be with the 3rd ground wire connected. That third ground is a rod into actual ground.
A lot of homes were built and are to this day still wired with only the two wires, hot and neutral. Yes you should use your grounded power cord with the turntable. Always use the best power cord you can, grounded or otherwise. My Herron phono stage uses a grounded power cord, even though you can see inside the ground isn't connected to anything. The cartridge is still grounded to the Herron even though the Herron isn't grounded to anything. (Not even neutral. Long story.)
So anyway, perfectly safe either way. Hum however will probably be lower grounded to the integrated. That way all paths to ground- cart and RCAs- are the same. Multiple paths to ground are an invitation to hum. Doesn't always happen but its a risk.
A lot of homes were built and are to this day still wired with only the two wires, hot and neutral. Yes you should use your grounded power cord with the turntable. Always use the best power cord you can, grounded or otherwise. My Herron phono stage uses a grounded power cord, even though you can see inside the ground isn't connected to anything. The cartridge is still grounded to the Herron even though the Herron isn't grounded to anything. (Not even neutral. Long story.)
So anyway, perfectly safe either way. Hum however will probably be lower grounded to the integrated. That way all paths to ground- cart and RCAs- are the same. Multiple paths to ground are an invitation to hum. Doesn't always happen but its a risk.