In a word, yes. The pumps could be bypassed by allowing the docks to drain through the filling culverts.
The dock would normally be kept dry and prior to a ship going in, the tie-rods securing the Caisson to the bottom of the dock were removed. Immediately before the ship was due to go in, the penstock valves on the filling culverts would be opened at the low water before. As the tide came in, the dock would flood. Once there was enough water to float the Caisson, the shore-side air compressor would be connected and the ballast tank would be blown. This would make the Caisson float up and once disconnected from the shore-side air compressor, it would be towed out by a tug and secured to a buoy in the river.
The ship would then be manoeuvred into the dock by a combination of tugs and shoreside capstans. Once it was centred in the dock, the tug would push the Caisson back into place, the ballast tanks would be vented and it would sink and be secured with large wedges hammered in from the top.
Once the tide started to ebb, the water level in the dock would fall along with the level of the river outside. A diver would be sent into the dock to measure the distance between the keel of the ship and the stalls on the bottom of the dock. When the ship's keel touched the stalls, the diver would give the signal and the penstocks would be closed. The dockside cranes would then be used to put the shoring into place and the shores would be secured in place with wedges hammered in. Once the shores were secure, the penstocks would be opened again to allow the remaining water to drain from the dock. The pumps would be used to pump out the rest of the water if the tide wasn't going to fall far enough to completely drain the dock.
Once the dock was completely drained, the Caisson would be secured with tie-rods to the bottom of the dock and the inevitable gap between the Caisson and the dock mouth would be caulked.
If the timings of the tide were not right or if they were in a hurry to get the ship docked, the pumps would be used to drain the docks instead of allowing them to drain with the tide.
This procedure was only used for Dry Docks 2 - 4. The other Dry Docks opened out into the No 1 Basin and they were always pumped out.