Data is inconclusive either way.
Unless you have a seriously poor running engine with leaky injectors, bad A/F ratio, no thermostat, and tons of blowby, I wouldn't worry about when you add the FI cleaner.
The well maintained engine in good running condition with a normal OCI shouldn't be affected at all.
We also have many products that are user dosed with every tank throughout the maintenance interval.
There isn't any massive failure of engines caused by FI cleaner, is there?
Time to grab a rental car, toss in a bottle of Regane into the 'oil', drive it a month and then pull a UOA!