Thought Experiment: (I'm using water for the immersion fluid)
Take a small steel cube and a small wooden cube same size. Place them in a
large balloon or ziploc bag - something big enough so that the 'elastic
forces' are negligible, but able to flex. Tie it off with a minimal amount
of air inside. Put the steel cube on the bottom.
Submerge this whole thing in water to some depth. What happens? Gut
feeling is that both cubes will be 'pushed' together and will not try to
separate. The 'glue' between them would be in compression. There would be
a contact force - solution B
Now put a hole in the balloon/bag to let water in. Now they will try to
separate. If they were glued together, the glue would be in tension. I
think this is the source of confusion with the difference between whether
or not water seeps into the glue.
Is this a fair experiment? No.
Both cubes will sink in the first fluid (air at any reasonable pressure
(hence density)). Only one will sink in the second fluid (water). The
buoyant force directly applied to each cube is from the fluid in which it
is immediately immersed, which changed when the hole was made. [There will
be an additional buoyant force applied to the bag/balloon when it is full
of air, which will be transferred through a contact force between the steel
cube and the bottom of the balloon/bag.]
Now replace the balloon/bag with a glue encasement. Although the question
does not address this, lets assume that the glue is also incompressible.
Then the density of the 'fluid' in which the cubes sit is the same as the
water - this is most similar to the case where the balloon has a hole in it.
New thought Experiment:
Consider the cubes as being just in water with a string between them - when
does the string break?
Free Body diagrams
Top cube:
Pressure force dg(H-L)A down
Pressure Force dg(H)A up
Buoyant force dgLA up
Weight (d1)gLA down
Tension T down
__________
dgLA+dgLA-(d1)gLA-T=0 T=2dgLA-(d1)gLA = constant
Completely independent of depth
Bottom cube is similar.
Is this a fair experiment? No.
The string model is not good. As the pressure increases (with depth), it is
reasonable to suppose that more water will seep into the glued space
between the two cubes. As that happens, the surface area available to the
glue will decrease. The 'string' will get weaker with depth, while the
force that it must supply remains constant.
I therefore contend that they will separate eventually- but there is
insufficient information in the question to obtain an answer. It depends
on how strong and how waterproof the glue is.