That kind of system has been tryied before and has the following drawbacks.
Eventualy the bag will crack ,leak or burst letting alot of water into a dry space without warning untill the casing is flooded.
With no releafe valve or means to divert water pressure when the bag gets full ,the bag is in great danger of litaraly exploding not good!
As these gear pumps can produce tremenduse PSI and make great hydraulic pumps as in the larger aplications.
A non positive displacement pump works much safer.
As the gear pump wears its internal tolerances increase and water flow will increase and the bag will fill very easily needing to constantly pump it out just to stay afloat,waisting power.
The best bag system i have ever seen and used is on the SB-1 by Thunder Tiger ,the hole system with its integrated failsafe and over pressure pump cut off along with low power surface feature and no signal surface function is a jem of a system.No valves are used as well but that is due to the type of pump,a paristolic pump acts as a valve in both directions and as a pump.
Sorry been there done that a long time ago.
