He did. He's pretty much been an alcoholic since the 80s when he first started with Slayer. He's known for being a notorious drinker.
I think both may have factored into it. He was probably already weakened from the alcohol and everything that came with the spider bite just made him worse (the medicines, blood infection, etc).
Regardless, it doesn't really matter. The guy is gone, but hell, he left one hell of a legacy behind. One of the founders and main composer of a band that influenced and transcended the genre as a whole (along with only a handful of other bands ie: Hellhammer, Venom, Bathory).
With that being said, I will link a video of one of their performances from back when they were the biggest (metal) band in the world. Incredible how fierce, hungry and rabid their performances were.
Every Metalhead needs to watch this. THIS is how Heavy fucking Metal is done. No bullshit.