You should race as you train - otherwise why are you training like that?
You're training to bring about adaptation to promote your body's ability to perform optimally in the task you're asking of it. If you're using a heart rate monitor to prepare for a race - whether it's 400m, 5k a marathon or anything else on the scale - then you're using the feedback to guide you.
We all know that race day is full of distractions, unusual situations, the adrenaline of competition so using a monitor will, I would suggest, be absolutely vital to allow you at least one dimension that you can control.
There's an old adage, "nothing new on race day" - normally this means no new equipment, so no new shoes that will rub in a new place, or a new gel or bar that might not sit quite as easily in your stomach or whatever. If you're not used to running blind (on speed or any other metric you normally track), then don't do it on a day when you are guaranteed to be feeling emotions that will make you behave very differently to normal.
So your HRM based training will have led you to a point where you'll know the target zone for your run. Definitely use that information on the day.