Advice on using a hybrid bike for first triathlon

The road tires are the biggest thing, so that's good.   I have seen hybrid bikes with clip-on aerobars.  You could try that... For a modest investment, it's worth a shot.

It will make the race more difficult for you, compared to those with road or tri bikes.    But if you're okay with that, I can say you'll definitely not be the only one on a hybrid (or cruiser, mtn bike, etc).

There is a lot of variation in hybrids. Some, like mine, have bigger tires that are treaded sort of like my car. Others, like your's, have narrow, slick, high pressure road tires. So I would think your's would do okay in a race. It'd be more uncomfortable leaning down to have less drag, so you'd either deal with the wind resistance or deal with an uncomfortable position. For a sprint either would work. I used to hold my handle bar in the middle and lean over somewhat.

You will be fine with your hybrid. Don't sweat it.

Smile.  Thank the volunteers.  Enjoy the race. 

You'll see plenty of hybrids at most tri's, especially sprints.  My wife did her first two tri's on her hybrid.  She did have clipless pedals and slick tires, same as you.  Also had some handlebar extenders put on at some point to help with climbing.  Otherwise there's not much else you really can swap out that isn't going to be more road bike geometry specific.  Enjoy the ride!

You'll be fine.  If you train hard on that hybrid, I would not be surprised if you pass some people on road/tri bikes. 

Tri bikes don't have little electric engines that hybrids don't have.  All the power is still supplied by the rider.