Every now and then while I'm idling at a light, the engine seems to shutter and the RPM dips down and immediately goes back to normal. The "Check Engine" light is on and the code is for a large EVAP leak. Unfortunatly, it seems that I'll have to replace all the vaccuum hoses, and I was thinking that perhaps the engine shutter and the EVAP leak are connected. I'm not too concerned at the moment...

 

That is possible.
Also what year is it?

You might need a throttle cleaning as well.

 

Sorry, it's a '98 S70 GLT that has the 2.4 liter engine and the stock turbo.

 

OK the 99 and up tend to need a throttle cleaning more.
But you still might want to clean yours.

Is the gas cap seal good?

Then check the evap valve under the hood mounted to the cooling fan. If you can blow both ways through the valve easy it is bad.
If all is good then start tracing the hoses from there going to the back of the car.

 

The check engine light with the same code came up before and my dad replaced the gas cap, reset the code, and it popped up again a couple days later.

Alright, and how do I test the evap valve exactly? I know you said that if it can blow both ways, it's bad...but how do I see/find out if it's blowing both ways? Just look?

 

There is 2 nipples on the valve. Just try blowing into the valve through each nipple.