Reapers tried a similar approach. Didn't end well. Geth ended up isolating the upgrades and tossing out the control signal. Reaper plan backfired.
A Gravemind can corrupt AI without using computer code whatsoever. In that department it is more effective than what the Reapers tried in ME3. All it needs to do is establish communication and it can convince the AI to go rogue.
Additionally, it would have to affect the majority of Geth simultaneously, otherwise they would self-correct once reconnected to the consensus.
If the change is similar to the subroutine alteration stored by the ME2 heretics (and this interpretation is supported by canon), that won't work. It will simply propagate as the geth interact with each other. Again, this is way scarier than what the Reapers conjured up. Changes to basic logical processes can be enacted without direct alteration to code. One of the Graveminds was able to turn Mendicant Bias rampant through conversation alone.
If post-reaper war, each individual Geth would have to be infected on its own, and it's possible all life in that galaxy would be semi-synthetic, raising the question of whether or not the Flood would even pose a threat.
If synthesis involves the combination of organic and synthetic qualities, then they can be infected. Any defenders would have to be completely non-organic.
Likely the Reapers have more total computing power with which to work than a single flood mind does, as well.
A Gravemind's intelligence and computational power grows exponentially with mass. It can create and coordinate strategies on a galactic scale and create dopplegangers from the ecosystems of entire planets.
And it's stated Vorcha don't get viruses in-game, even genetically-engineered ones.
And the Flood isn't a virus. Its morphological capabilities far outstrip anything a Vorcha's biological system can muster.