Phono grounding when using integrated w/ floating ground?

It should be fine, and NEVER disable a ground pin from an AC plug. :)

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.

@ lostark

You don’t need the AC mains safety equipment ground.

The ground for the TT arm is the circuit ground of integrated amp.
Just connect the ground wire from the arm to the ground lug on the amp.

Jim

So your integrated is grounded,

Not necessarily. If there is no chassis ground, and the live and neutral are isolated by the power transformer in the amp, then there is no safety ground or direct path to true ground. The manufacturer has ensured the amp is double insulated and does not require a safety ground.
In your set up, the amp would be grounded through the turntable ground wire only; thereby ensuring no ground loop.