The countdown on the Genesis device is not like the timer on a bomb, where if the countdown is stopped before is reaches zero, nothing happens because the bomb has not been triggered. The Genesis Effect has started operating as soon as Khan activates the timer.
This is clear from several things that happen. You can see in the clip from the film that as Khan goes through the four-step activation process, the Device is progressively powered up.
However, when he finishes the last step (at 4:26) the Genesis Device starts to operate. The behavior of the device has changed. It's not just lighting up any more; it's outgassing as it runs.
Moreover, while the above argument, based on the appearance of the Device, is certainly not conclusive, the next scene definitively states that the Genesis Effect is active. On the Enterprise, Spock immediate detects that the Genesis Wave is already being emitted.
SPOCK: Admiral, scanning an energy source on Reliant, a pattern I've never seen before.
DAVID: It's the Genesis Wave!
DAVID: They're on a build up to detonation!
KIRK: How soon?
DAVID: We encoded four minutes.
KIRK: We'll beam aboard and stop it.
DAVID: You can't.
This indicates that the Genesis Effect is already active. Apparently, it takes time between the start of the effect and the sudden burst of new life (which the builders arranged to be about four minutes). In the meantime, although some of the Genesis energy involved is leaking out, the simplest explanation for what is happening is that the Genesis Device is creating and storing most of the energy, which will all be released at the time of "detonation."
What would happen if the Reliant, or the Genesis Device aboard the Reliant were physically destroyed? We don't know for sure, but that stored Genesis energy isn't just going to be obliterated. If the device is blown up half way through the countdown, maybe only half (or less) of the total intended energy will be released. However, even a half strength Genesis Effect would be more than sufficient to obliterate anything nearby, including the Enterprise. (On the other hand, an uncontrolled partially-powered Genesis Wave detonation might be more destructive than a controlled one. We just don't know.) But either way, the Enterprise needs to get out of the neighborhood, so the crew (with their ship in almost crippled condition) are not going to waste time on anything else, like a pointless salvo of torpedoes.