Can I monitor tracks recorded in my DAW through the Konnekt 24D headphone outputs, overdub vocal parts back to the tracks while hearing the tracks and my voice, all without latency problems?
Yes, this is certainly possible. The DAW channel (main stereo output of your host application) comes up in the Konnekt mixer along with the signals coming in on the inputs.
This allows you to use the Konnekt mixer to create a headphone (or monitor) mix, of both pre-recorded tracks and the signal coming in on the mic input (all without latency), and monitor it through the headphones.
More information can be found in the manual of your Konnekt interface.