I suspect they do, but I know they don't intentionally seek them out (thank goodness) I have seen where its only a "stump" left where a 'shroom was growing and feel certain a deer done it. But I have also seen where they have stepped on them and didn't bother eating it, along with many other morels right off a deer trail. Oddly enough, it seems where ever morels grow, its always deer sign. That could be due to the fact morels grow in the most fertile soil in the woods, along with lots of other desirable plants and its just coincidence that deer use those areas.

And by the way, the half-free morel you are holding is an above average specimen LOL I know I've never found one that size! So you may have found a real "honey hole" both for morels and deer. It seems deer love swampy areas too.