In the past, I've complained that the first word or two of a transmission often gets missed. One theory was that the tuner (RTL dongle back then) was taking some time to effect retuning, and that a solution that doesn't need to retune may be better. I'm still noticing the start of transmissions get missed occasionally, but maybe less than before. I might have to go back to the RTL to try to get a comparison.
When you said "doesn't work that way", perhaps you meant that it doesn't continue decoding the control channel whilst simultaneously decoding a voice channel? I believe that that's true, although it does monitor control traffic on the voice channel.
I'm not sure if there's any latency involved in "offset retuning".
~iain