Thanks for all the replies. To be clear, they are sapsucker holes which only go down through a growth ring or two, I'm confident that the vast majority of the sapwood is sound. I cut the tree myself and I'm sure it was living, it wasn't a bird trying to make a nest.
Thanks for the anecdote, Bryce. That was the sort of thing I wanted to hear.
Del, I appreciate your caution and a healthy part of me shares it. I wonder though if the woodpecker holes are a bit different in nature than the bug damage which I assume happened after the tree was dead. With the woodpecker holes the tree was alive and therefore had the opportunity to heal around them somewhat. That, of course, could just be wishful thinking on my part but it sounds nice.