When is the LTC4311 current source activated?
I think that the current source operates when the threshold value (VTHR) is exceeded.
The VTHR is spec is part of it, we also need to look at the SRTHRESH spec. It needs to see the line voltage rising at a certain slew rate while crossing the threshold to turn on the boost current.
The LTC4311 idles when the bus is high. Its well suited for battery powered applications because weaker pull-ups can be used while still maintaining data rates.
And it won't be in contention with any of the devices on the I2C bus trying to pull down. Its only active for positive bus transitions.