What is the purpose of the Denon receiver?

Connect the Beam to the TV’s HDMI ARC port. Connect the Blu-ray player and Denon to any of the TV’s other HDMI ports.

I was thinking the denon would be used as a switch between various input  devices connected to it and direct their audio to the soundbar. 

With your suggested setup would the AM-FM radio of the receiver be heard on the soundbar?  How about other devices connected to the denon?

The denon has an input for blueray player so I am assuming if I connect the blueray player to it, it could send video to the TV and audio to the soundbar.  Is that correct?

Full disclosure: I’m not a DENON user. In general A’V receivers cannot route analog audio (AM/FM) to an HDMI-ARC port. With respect to Radio, most stations have Internet streams that SONOS can access, however, the stations do not usually stream major league sports events over the Internet.

Your proposed set up is unsupported. Sonos expects the TV to be the switch for all your HDMI connected devices. You could use a real (ARC enabled) switch if your TV does not provide enough connections.

Two observations:

1. using a receiver as a switch for me is a waste of a good receiver (and electricity);
2. the ARC on the Amp is expecting an “in” sound stream, while you want to use it as an “out” to the Beam - not sure this will work.

In many cases a cheap A/V receiver used as an input switch is less expensive than a fully capable HDMI switch -- go figure.