No, it's not like a balloon, an eruption isn't the earth popping, it's an upheaval from the mantle eventually surfacing through a weak spot that causes it.
Anything to relieve the pressure can, by definition, cause an eruption if there is an inadvertent feedback loop.
For one, the scale is way, way too big. It's like stabbing an elephant with a needle and expecting it to bleed out.
Also, the dangerous type of magma is extremely viscous and gas-rich. It doesn't flow like Hawaiian lava does.
If you want to move lots of heat away fast, you either need a big pipe or a very high flow rate.
“Gas-rich”, to me, also sounds as if it would be more dangerous.
Gas-rich is where the danger is, as I understand it. Those gasses expand as they get closer to the surface, and if they're trapped in viscous magma that doesn't flow easily and puts a lot of stress on the rocks above.
The fluid basaltic lavas of Hawaii don't explode, they flow out and make shield volcanos.
Check out geologist Shawn Wilsey's videos.