I use a station, not a particular song but I tried your scenario and here is what I found. First, alarms are device specific. There is not a default alarm tone or song for all your echos, each must be set up individually but can be set as a default for that particular echo. Second I think that this has to be initially set up by voice and then can later be modified in the app. So I asked one of my echos to set a re-occurring alarm at xx:xx time to Wipe Out by the Surfaris. It then asked if I would like to make this the default alarm tone from now on on this device which I agreed to. Next I asked to set up another alarm with just the time and again it played Wipe Out as it should. Now I tried to set an alarm for the same echo using the app and Wipe Out was again the default.
So yes, what you are looking for is possible.