If the aerial signal passes through ANY other device, HDR-FOX T2 box being one such, then the signal can be interrupted.
For environmental reasons the HDR-FOX T2 has a default setting to not pass the aerial signal through to the TV when it is in standby. This is to give the lowest possible power consumption in standby. If you want to view live TV with the box not fully on, then you can go into the menu settings to turn the low power standby OFF, which means it will pass the signal through all the time (unless you turn the box off completely at the switch or socket). You'll also have a slightly higher electric bill
If you watch live TV without the box you won't be getting the benefit of being able to pause it, so for general use it makes more sense to use the box to watch live TV anyway, in which case the low power standby is not an issue.
On those occasions that you have to use the TV direct (when the box is doing recordings that prevent you selecting the channel you want to watch live) then the box is on anyway, so the signal is being passed through.