No, the saw ‘blade’ was a diamond impregnated cable. It could not have closed off the flow.
Before the saw cut, the main casing was cut of about 75 feet away from the bent and leaking exit of the BOP with a giant shear which basically pinched the 21" pipe flat. After the diamond saw got stuck near the top of the BOP, they gave up on it and again used the TWENTY THREE TON SHEAR to cut the rest of the casing. Both of these actions may have created a huge "water hammer" pressure spike that may have destroyed the already damaged casing. Not to mention the beating from using a 23 ton device similar to bolt cutter hung from a 5000 ft cable.