Dude...I am very similar in style: I attempted the first playthrough (and currently 2nd) with zero covenants and zero invasions from me, and avoided getting invaded as much as I possibly could...even not logging online at times.
What I found differently, however, is that the most intense parts of the game, even more than the best boss fights, have been the PvP. OTOH, I'm primarily Faith/Strength/Agility and low weight so I can roll around a ton and prolong battles, drink Estus, and I almost always win a battle of attrition...In fact, I never lost a PvP battle until I started soul farming at the Giant Lord in endgame of playthrough one. As much as I hate the 15 minutes of unplanned segue that an invasion typically is, my heart is like 200 bpm the entire time, and it's fun. But remember, you can play starting out disconnected, and you won't have any problems with PvP invasions; OTOH, you'll have more (and much easier) PvE invasions.