No, availableForWrite behaves the same way as flush() on Serial2.
I believe it's a problem in how Serial2 works on the P2/Photon 2. All of the other ports uses a dedicated UART peripheral, but Serial2 uses the generic high speed serial port, which is also used for SPI. It appears that it behaves differently.
Serial3 shares the same pins as SPI, but Serial3 uses an internal pin mux to switch the port between the dedicated UART peripheral and the SPI peripheral, which is why that behaves differently.