i think the general consensus is that coffee would raise cortisol levels after waking up - especially with those who have impaired metabolism. but i think it's also generally agreed that eating diminishes both the AM cortisol as well as the potential cortisol spike from drinking coffee.
You can always experiment with temp. and pulse to see the effect - upon waking - and then 20 min. after drinking coffee alone - or 20 min after eating something and drinking coffee.