Dry sponges placed in flowing water (as opposed to water source blocks) have no effect on the water and remain dry.

To reproduce:

1. Place a water source block on a flat area and allow it to spread
2. Place a dry sponge block in the flowing water at least one block away from the water source

Expected result:
The water surrounding the sponge is removed for several blocks, including the water source so that all the water disappears. The sponge becomes wet.

Actual result:
No effect on the water at all. The sponge remains dry.

Edit (and facepalm): If the sponge is placed in the source block, the effect should spread to the flowing water but does not. Flowing water is just not affected at all by the sponge.