Thanks for the interesting question. We have the Pomodoro-style time tracking request in the Uservoice for some time already. So far, it does not quite look very popular.
Personally, I use Pomodoro technique for myself from time to time. In most cases, I use it just to focus, and not to actually track time and to associate the time spent with particular tasks. The technique itself is very good, at least it works for me.
But I never felt the need to add time tracking to Checkvist directly, I use a separate apps for that (and I never track time for particular tasks). My current favorite app is Forrest.
If we add time tracking to Checkvist, the next logical step would be compare estimated time with actually spent time, some reporting and so on. Would most Checkvist users benefit from this? So far, not so sure.
Hope I answered your question, though probably not quite in the way you expect