Will I need two expansion vessels in a closed system design if the
boiler doesn't have an internal one?

That will depend on how the circuit is implemented and the boiler chosen. It
isn't clear from the schematic what the two different flow and return lines
from the boiler are. Are they isolated circuits? Are they just two outlets
from a diverter valve on the same circuit? (i.e. similar to a
Worcester-Bosch system boiler with the optional internal diverter valve).

You may need one anyway, as the water content of such a system might be so
high that a boiler internal expansion vessel wouldn't be big enough to
contain the pressure rise.

Christian.