In Star Trek: Generations, it was this very thing that destroyed the stardrive section of the Enterprise-D. As soon as LaForge recognized that a coolant leak had occurred, he evacuated Engineering immediately and reported to the bridge that a warp core overload was inevitable and irreparable. Yet in the very next film, Star Trek: First Contact, Picard suggests (and Data supports) causing a massive coolant leak in order to eradicate the Borg infestation there.
Two reasons come to mind:
In Star Trek: Generations, the engines were hot because of the just completed Battle of Veridian III. In Star Trek: First Contact, the Enterprise had been quietly orbiting Earth for some time. Cold engines are presumably in less need of coolant.
The Enterprise-E was an upgraded ship compared to the Enterprise-D; it is not unlikely that some of the changes were intended to mitigate the warp core breach problem that had destroyed the Enterprise-D. In fact, we can see that the Enterprise-E has two plasma coolant tanks in main engineering. Only one was damaged; perhaps that redundancy prevented any core breach.
It is reassuring that my thoughts are echoed by the article on plasma coolant in the Memory Alpha wiki.
The short answer is that it wasn't the coolant rupture (in Star Trek: Generations) that seems to have led to the warp core explosion, it was the failure of the magnetic interlocks within the warp core. The coolant leak was a secondary issue, and one that resulted in Engineering being evacuated, but this seems to be more to do with the health of the staff than the health of the engine
We see a similar issue in DS9: Our Man Bashir.
WORF: The magnetic interlocks are failing... a warp core breach is imminent.
As to whether the loss of coolant was an issue, it may be stating the obvious that there are two plasma coolant tanks. Data only broke one of them. It seems likely (in fact downright certain) that the Enterprise-E can survive on only a single tank, at least for the amount of time needed to effect repairs.
PICARD: The first thing they'll do in engineering is establish a collective, a central point from which they can control the hive. The problem is if we begin firing particle weapons in engineering there's a risk we may hit the warp core. I believe our goal should be to puncture one of the plasma coolant tanks. Data? - Chakoteya - First Contact Transcript
This is backed up by the film's official novelisation
He moved over to a large display padd, activated it, and called up a schematic diagram of Main Engineering. “The problem is, if we begin firing particle weapons inside engineering, we risk hitting the warp core. So I believe our goal should be to puncture one of the plasma coolant tanks.” He tapped another control; the schematic rotated and zoomed in on a diagram of the warp core with two flanking coolant tanks, each marked with a flashing biohazard symbol.
The Galaxy Class Starship was sensitive to warp core breaches given they only had that one large coolant tank in the back of the room wrapped in insulation. On both TNG and DS9, they went through dozens of destroyed Galaxy Class Starships.
The Sovereign Class Starship is more advanced with the two coolant tanks.