Yes, it is possible to use Alexa to control the Play:3.

In the Alexa app under Devices, have you tried to add the device and allow the Alexa app to discover the device? If Alexa can’t detect it, you might try unplugging the Play:3 from power for a couple of minutes and reboot your router and phone.

Note, however, that as the PLAY:3 has no built in microphone, you’d need to be using an external voice activated device to control the Sonos system, either a Sonos device with a mic, or an Alexa device itself. 

Hi, 

I've been having similar issues connecting my Play 3 and so far haven't found a solution. I'm coming to the conclusion that it's not possible, so would be grateful to hear from anyone that has actually succeeded with the Play 3.

Alexa and Sonos accounts are linked in the alexa app, and my Play 3 speaker is recognised on the system during setup. However, alexa still won't play through the Sonos. 

When I try to add voice assistant in the Sonos app it takes me to the alexa app, where it appears all is setup, but it clearly isn't. Also, when I go into my specific alexa settings and try to change the default speaker, my sonos play 3 is on the listed, but greyed out and unselectable! The help says that 'for a speaker to work with an echo input, it must be able to play all audio. Your preferred speaker is only available to certain types of audio, like music and audio books'.

So maybe it just don't work! 

The Play:3 is an old speaker and does not have built in Alexa.  Please read @Airgetlam ‘s earlier reply on this thread.