Nope. Unless you get hardware or find some special software to mix the two streams, Discord only supports reading input from one audio stream. If your goal is a like a radio or something, perhaps see if it's possible to multi-instance discord and just have another account that stays in chat with you - but the client it uses is configured on stereo mix.
But yea, basically, you don't get that kind of mixing in any of the chat programs I'm aware of.
I mean, I guess you could set "listen to this device" on your microphone, but then you'd be hearing yourself talk with a slight delay which might get a little jarring. The reason this works is because it means what you put into your mic is reflected out as audio, and hence stereo mix captures it.
There is probably some sort of software that allows you to create a virtual sound device that enables this kind of mixing, but I do not know what it would be and there would almost certainly be a delay between you speaking and the audio happening.
I would look at audio mixers. There's a hack you can do for mic input where a 3.5mm M->M cable from output to input acts as if you were speaking into it.... the trouble is that you would then need to merge your microphone input into that signal.
If you can find an audio mixer for cheap, you've got a probable way of doing this - perhaps look up some DIY options? Basically you need something that can mix the microphone input signal with another input signal (in this case, a 3.5mm coming out from your case) and then feed that into the microphone slot. For your own audio, you'd simply use a headphone splitter (with one going into your headset, the other going into the mixer).
Edit: Something like this **might** work. It has to take 3.5mm inputs and do a 3.5mm output. It's janky though.
Aliexpress ($28 CAD)
Ebay.ca ($25)
You'll want to confirm this with the sellers, and I will warn you it may be a bit sketch if this works. In theory it should.... You would also need a simple 3.5mm splitter cable, and a 3.5mm M->M cable (this often comes with decent monitors if they have integrated speakers) so that you can pump output from the PC to your headset and to the mixer.
In theory, the wiring is something like this (note: yellow is just to make sure you know what has what ports - it doesn't represent any cable or anything):
Though I would make sure to test if my assumptions are correct using your headset + PC ports (use something like audacity to test recording) to ensure I'm right about how this all goes down.
Your headset must also have some way of outputting to analog for the mic. If it uses a single 4-pole, you'd need a 4 pole splitter cable. Any cables I've mentioned are easily had on Aliexpress for a low price.
Edit #2: Or a simpler solution - if you don't mind sharing desktop, it now supports sharing audio. This only works in calls though, not servers.