No. On both the 396XT and the 996XT the backlight turns on when the squelch breaks (if that is the backlight setting you choose) and turns off a few seconds later. There is no way on either scanner to change the time.
I too wish that it would stay on for the entire duration of the transmission, but I'm used to it now. On my 396XT I leave it set to "infinite" and turn it off and on manually (tip: set different alert tones to your more important channels so you know what you are listening to without looking at the scanner. On the 996XT it really isn't an issue anyways; since the radio is powered externally I just leave the backlight on all the time (you can easily turn it on and off as well as change the brightness by simply pressing the volume knob).