Can you have your do not disturb function on and still have an alarm on???

pretty easy to test this right?

Go to Settings > Focus > Do Not Disturb, turn it ON

Go to your Clock app and set an alarm for 1-2 minutes later.

Wait.

For me, I turned off Silent Mode and the alarm came thru

Yes, I am pretty sure that "Do not disturb" is only for incoming calls.

Once you have "Do not disturb" active your phone will not ring, it will just put your calls to answering machine.

But in saying that Apple has made it that if the same caller calls you twice on the second call it will ring.

I hope that I was able to help!