Partially. The relief wells are supposed to lower the pressure, but their main purpose is to allow them to start pumping heavy drilling mud into the bottom of the well and basically plug it at its source. Doing so will more or less kill that well for all future use, which is a bigger economic hit to BP (although frankly dwarfed by what this is going to cost them overall).
You have to remember, when this all blew up, they were in the process of pumping mud into the top of the well to "cap" it for later use.
To use a DF analogy, they dug down till they hit cavern, just so they'd know where the platinum, gems and HFS metal are for later. Then they were going to build a microcline wall to seal it off and come back when they're ready. But instead, oil demons with [BUILDINGDESTROYER:1] poured forth. And then, they had two options:
1. Try to fight their way back in and build another wall, hoping that there wasn't a gap somewhere else they had missed.
2. Cave-in with semi-living rock. More likely to succeed, but then they'll never be able to dig back down to that deposit.
They've been opting for #1 for quite a while, partly because #2 was going to take a while to set up, and partly (IMHO) because they didn't want to lose the chance to extract that oil later. I think what changed the equation somewhat might be best illustrated with a DF analogy as well:
Barack Obama, President is throwing a tantrum!
Tony Hayward, CEO has been struck down.