Although I carry my 1520 on the bike, I have always used my work phone or my Sony MP3 player with headphones/headsets.
Been using a set of headphones with a mic recently (Tend to have my work phone plugged in as I need to answer that for work) so just plugged that in to my 1520, I had to click the mic button to say "Hey Cortana, call XXXXXX" and it worked, the real test will come tomorrow when I test it on the bike, but because I have had to use the mic button its not a "Hands free" solution so best wait till traffic lights before making the call, you normally need to press the same button to answer a call as well.
Up until recently I used a Bluetooth headset by Scala, I could answer calls on this by making a noise like saying "Answer", but it packed up and I am not buying a new one so unless my company replaces it, its just headphones, but it was always connected to my work phone so never tested with Cortana.