Yes. It's difficult to sum it up in a nice, tidy, technically precise way that isn't open to nit-picking, but I'll make it as succinct as I can:
Mean Sea Level, still water depth, and the half tide level are all different. Mean Sea Level is a datum based on the previous 19 years of data. So unless sea level rise is linear, it'll be a bit slow on the uptake in reflecting the current conditions. Still water depth is the level at which the surface of the water would be at a given point in time in the absence of wind driven waves. Half tide is the average between the mean high tide and mean low tide.
So the average still water depth would be roughly equal to the half tide level. I say roughly because it also accounts for storm surges and other variations beyond periodic tides. The fundamental premise of sea level rise is that the average still water depth is trending up. Therefore, the half tide level would also be trending up.
Sea level rise isn't necessarily causing a change in the tides - I'm not aware of any research showing that tide ranges are changing, but there's more water out there and so the average level is higher. That's why in coastal cities we're getting more and more nuisance tidal flooding. At high tide, storm water drainage systems don't work as well because they're either being back flooded or their check valves are held shut by higher water levels at the discharge.