No, the only two Sonos devices that can use Bluetooth as a source are the Move and the Roam.  Of those, only the Roam can transmit the Bluetooth source to the other Sonos speakers.  

To my knowledge, the only turntable that connects to the Sonos system wirelessly and directly, not using Bluetooth, is the wildly expensive Victrola. If it were me, I’d either go the route suggested by @jgatie above, or add a Sonos Port or Sonos Five to accept that turntable’s line level output via a wire. Once the signal is in the Sonos ecosystem, it can be sent wirelessly to any connected Sonos ‘room’. 

Thanks for the quick replies friends! I saw that Victrola as well but it is indeed very pricey. I found this cheaper (though still expensive) record player on Seth Rogen’s site Houseplant. It has bluetooth capability but it seems the main issue is the particular Sonos speakers I have. I was hoping to get something less than $400 but it seems my options are limited to what you suggested jgatie.

Thank you both again for the help and take care.