Can a round-over router bit do 50% of the thickness while resting on the cut profile?
Adding a full round-over edge (bullnose) to plywood of the type that you have pictured is questionable in my mind. Typically such edging is applied to solid wood pieces. The plywood may very well have tearout along the edges where the grain is at odd angles. This can be somewhat mitigated by using the very best router bits that are extremely sharp. 

You will want to fix up parts of the edge, such as shown here, before you attempt to cut the radiused edge. You will want the transitions to be very smooth and once cut would be much more difficult to correct.

 

Rounded edging on plywood is usually confined to the type of plywood that has many more layers such as this baltic birch plywood with void free core. 



And finally the rounded edge that would most often be found on such material will use a different profile than a full round bullnose.