I tried this exact same thing yesterday.
For my test pieces, I used a section of cotton drill and a section of poplin, which is (apparently) a lighter cotton type of cloth. These were adhered to a piece of 4.5mm vegtan.
I tried a section of contact adhesive and a section of Titebond lll PVA, with a piece of flat acrylic and heavy weight on top of the test pieces.
The contact bleed through the lighter 'colour and weight' material, and was a definite fail. The Titebond lll PVA did not bleed through.
The heavier cotton drill, which was a darker camo pattern, did not bleed through at all.
Interestingly, neither adhesive appeared to affect the flexibility of the leather, but I did notice where I had applied the Titebond lll past where the cloth covered, the dried Titebond lll cracked when the leather was flexed.