floating ground on ICs?

That would be a floating shield, not a floating ground. It's not a safety issue because you have to have a ground connection from one component to the other with single ended connectors or it simply won't work. It will however hum very loudly.

At a minimum you need 2 wires. The hot from the center pin of the RCA and a return (or ground) from the outer. Without these 2 it won't work. Some cables also have a shield around them that can be connected at both ends to the ground, or connected only at one end, or not connected at either end for that matter, but usually either one end or both.

Since you are building your own I would try it both ways and see if you can hear a difference.

I don't have any idea how many do it but it is an accepted practice. Since you are building your own you can easily incorporate small switches in a pair so you can connect/disconnect the shield to see if it makes any difference. Some claim it even makes a difference which end is floating.