Fail, blocking off the spawner doesn't do anything, just place torches on all 4 sides of it, it'll stop spawning. After that, you can build a trap around it kill it and carry the drops to a safe area. :p
Also, a mining tip: when you reach bedrock, start mining 1-wide tunnels, 2 blocks apart, parallel to each other. Quickest, most effecient way ofmining with missing anything.