RE: Display Port to HDMI
DP supports audio, although the spec doesn't require it (or even video, for that matter) - audio and video signals are optional. (Audio is optional with HDMI, as well.)
DP to HDMI requires an active adapter, meaning it needs to be powered (power can be through DP). If DP source (GPU) has an audio signal and active DP to HDMI adapter supports it (it should), then the HDMI should also have audio.
DP++, aka Dual mode DP detects whether DP or HDMI is connected downstream and switches accordingly. This means only a passive adapter is required. If your GPU supports DP++, then you should only need a passive DP to HDMI adapter. DP++ should also support audio.
So, DP, DP++ and HDMI specs all support audio.
One question is whether Dell implemented or hooked up the audio for the Optiplex 3020 Micro DP jack. (I believe the integrated Intel HD 4400/4600 graphics chip supports it, though.)
The other question is whether the 3020 GPU supports DP or DP++. DP needs an active adapter, DP++ a passive one.