Noah's Marine has half-sheets of core-cell at good prices. They can ship.
It's perfectly OK to piece it together.
The function of the core is to keep the skins a constant diatance apart and
to bear shear loads. Cored panels as they are thicker in section are stiffer
than solid glass panels. Foam cores need help in this only where there are
heavy compression loads, as from fastenings.
The drawback of plywood core is that when water gets to it, it'll rot. And
it's heavy.