If you're talking about the baseband firmware, that has zero effect on wifi. It's only for the cell radio.
When this happens, it would be interesting to see the Wireshark caps. Note that some apps can still explicitly use more data when on wifi than when not. I know as one example, Skype REALLY misbehaves in situations where multiple devices on the same network behind a NAT firewall are in play. No firmware can protect you against such situations.
As an easier option than Shark - when this is happening, turn the screen on and off a few times and take a dmesg. Look for the following happening repeatedly:
bcm4330: early_suspend processing disabled, suspend_disable_flag is set by system.