Had some thoughts on why we have to attend this fight as the 'boss' even if we don't want to ( And don't give me that "It's Part of the Experience Just Play offline hurr durr durr" crap-fest )
I tested getting summoned to this covenant. Here's what SEEMS to happen: if you are NOT in the covenant, once get you TO the city (Moment you get carried across by the harpies) you automatically get the equivalent of a number out of a hat. If your 'number' gets called you go be a spear for somebody in your standard summon/invasion range. This is for all covenants and even applies to people who are not in any covenant. Once you HAVE done it your chances lower dramatically. You increase your chances of being a spear (at any point, before or after already doing it) by putting down EITHER color of summon sign, though white summon signs seem to have slightly higher odds. Red Eye's also raise your chances significantly. If you revive Judicator Argo via the Purging Monument you take a number out of the hat again. It is possible to be summoned more than once as a spear without doing this, but can be considered rare. I made four different characters and tested this at SL 88 99 120 and 140, I can't supply solid percentages on your chances, but this information is from my repeated testing and ovservation.
The chances of being summoned to this covenant while NOT a member are only low when your Soul Level and Regional Play settings don't have many people who are actual members. You can even actually obtain the highest covenant reward without ever actually joining (Should be obvious since you can drop off the ornaments without first selecting the "ask to join covenant" option) and it isn't pointless to do so, even though the covenant fight is the only place that the covenants rewards can even be used, you can basically BE a member just by continually fighting Halflight offline then going online, putting down a summon sign (Places that are OFF the trodden path work better, so y'know, not two steps from a bonfire) and if you wait about two minutes you'll get summoned (roughly 5 minutes being the longest it ever took me, and I was halfway through fighting Ledo... KMS...)