You can use an RCA-Y cable to share the turntable output. Note, however, there will be a 75ms time offset between SONOS and your traditional setup.

You will want to use the turntable's internal phono-preamp and connect it to a Line-In connector (not the Phono) on your traditional setup.

You don't want two phono amplification/equalization stages in the signal path.

Just a slight correction regarding using the Pro-Ject Debut Carbon Turntable’s internal Pre-Amp. I have the same turntable in Black. The Internal Pre-Amp can be disabled to allow you to use the Phono-Amp input on your traditional setup. I have the internal pre-amp disabled in favor of a Cambridge Alva Duo pre-amp.

I would purchase a Sonos Port and connect it to Tape-in/Tape-out to send turntable music to other Sonos speakers. 

Yes that will work if not using a Y cable, with the Y, the internal preamp (or an external one) is needed as Sonos doesn't offer a phono level input.

Aside from that, splitting the phono level connection will present a load to the cartridge that may be a problem.

Thanks. I have an old port set up linked to a CD player in my studio. I’ll give that a try as well.