How are your turntable interconnects wired now? What are you using for a phono preamp? If you're using a balanced phono section with RCA inputs and have kept the pickup arm ground separate from the signal ground, you're probably already enjoying the benefits of the balanced circuit. Changing to XLR connectors won't change anything. And many balanced components do indeed deliver 6dB better s/n (or 6 dB more gain, if you prefer to see it that way) when run in balanced mode. For example, here are specs for the ARC Ref Phono 3 SE:
Gain:
Selectable 51 dB (Low) and 73 dB (High) at 1kHz BAL; 45 dB (Low) and 67 dB (High) at 1kHz SE.
(Note that the ARC has RCA inputs only.)