I would think that as long as your chest is under water then you would receive maximum resistance which is one of the aims of water running. For increased resistance you could wear a shirt or something else that would create drag. It also depends on your goals.
The number one reason, that I have seen at least, for doing water running is that you get a no impact workout that mimics running more closely than anything else available. This makes it the ideal option for cross-training when you have an injury that forces you to non-impact activity.
The issue with doing it in a pool where you would be touching the bottom is that it is no longer a no impact workout. If your reason for doing water running is to avoid high impact and not to avoid all impact, this could be a good choice. If your reason is to avoid all impact, if you are touching the bottom, there is obviously going to be some impact. Other than that, I don’t know why the workout itself would be any better or worse.