Can creepers destroy spawners

Well, Creepers can blow up stone and cobblestone, both of which have blast resistances of 30. Since a spawner has a lower blast resistance of 25, it can certainly get taken out by a nearby Creeper blast.

I suggest closing off side tunnels and keeping the area very well lit while you are nearby doing any mining or construction so that Creepers can't spawn. Then remove the lighting near the spawners when you are done (so they can start spawning again).

Yes, (non-charged) creepers have a maximum blast strength of 56 (at point blank range) and monster spawners have a blast resistance of 25, so the explosion can destroy them.

To combat this you can fill the area with water before you fully seal it, as this will reduce the blast strength of the explosion to 0.

As a side note, ghast's fireballs have a strength of 16.42, so cannot destroy spawners.

Sources: Creepers, Monster spawners and Explosions