What Pete (Curly) said! When wood is veneered about 1/8" or so and layered onto solid wood, it will stay, but just a tad beyond that in thickness, solid wood from 3/8" and up - glued or screwed onto plywood will crack. That is Mother Nature in action. You are not going to stop it with those methods.
My first two tables from 45 years ago are still around and both have cracks in it because I did exactly that and did not understand wood movement. A friend has one and a daughter has the other. They overlook the "mistakes" and claim that the tables have "character".
There are ways around it to allow it to be firmly attached and for the wood to move. Search for "Attaching solid wood table top to a frame to allow for wood movement." You will get two or three primary methods with more minor versions of each.
Edit in: - Also, there seems too be a specific size (smallish in size) in which you can do what you planned, and it will work but at what point, I don't know. For instance, I see people making checker boards and chess boards along with cutting boards with solid blocks of wood and sometimes put a base on the bottom and solid trim around it. For some reason smaller pieces such as a cutting board / chess board sizes don't react the same way but somewhere around 2ft by 2ft and above, movement makes itself known!
The plywood will resist movement but the solid will move seasonally and it will either curl concave or convex with the plywood bending. Or the boards glued to it will shrink and crack. Or the boards will break free of the plywood. I suggest you research wood movement. Try this shrinkage calculator and see how much the pine will move with just 1% moisture change. http://www.woodbin.com/calcs/shrinkulator/
