@MrsD
The Echo (since the newest firmware upgrade of the past month) can now SEND a bluetooth signal to a BT speaker or a BT receiver unit. (Previously the Echo could only receive BT signal, so this is an improvement.)
Nevertheless, an Alexa device cannot play music directly on the device speaker and simultaneously to another device via BT. For the most part, this is a characteristic of most BT devices. I believe the best you can do is have the current FW on the Echo (you likely do) and pair the Echo BT with the receiver BT. Now, you can be playing the Echo, move to your stereo by telling Echo to "connect bluetooth" so it connects to receiver so it plays on stereo via receiver. When you are back at Echo to listen again, tell Echo to "disconnect bluetooth" so sound comes out Echo again. You may have an issue where the receiver auto connects to Echo again when you do not want it to. In this case, turn power off receiver.
Using the new BT send feature of Echo, I have done something similar to this. Since my Echo is near front door, I have placed a BT speaker on front porch and sent music to it from Echo via BT (but then, the Echo stops playing through its speaker.)
@ tuicemen
Your suggestion is about BT speakers, and MrsD did not ask about speakers. She asked about a BT receiver connected to stereo.