Probably rife with spoilers if you haven't read all the way to chapter 42
Here is what i remember:
It's stated that only about 50% of the alicorns have joined red eye under his promise of mates. -Chapter 42
It's also stated that alicorns in the absence of the Goddess become much more individual and remember their former life. -Zebratown and Canterlot.
Insanity from the Goddess' absence is only theorized by Remedy to be a problem with really old alicorns (my guess is 100+ years). -MAS Cellar
My list of head-canon and pet theories:
From the "Touched by taint" perks Littlepip has I presume that radiation heals them to some degree. Plus it makes them faster and stronger when in radiation, pump 1000 points worth of rads into one and they become a super alicorn.
From Chapter 42 my guess is only the telepathically strong Green ones have the ability to create a new hive. And their consciousness would meld together into a fresh hive-mind preventing individuality. And even if they are telepathically strong it still required several dozen to force Littlepip to aim at Remedy.
Purple and blue aren't based as heavily on Gestalt and Mosaic as the green would, and their telepathy is probably bound to talking to others and empathy (only around other Pony races). And they would probably spread out Mariposa super mutant style, think Mean Sonofabitch and Marcus. What they would do after that is probably dependent on several factors including, former life, 'Goddess abstinence', character alignment, and just plain old plot necessity. For example some who were former raiders would probably continue reap havoc, some might start communities like Jacobstown and Broken Hills, probably mixed in with ghouls and other misfits.
While the goddess was alive any alicorn would have access to any spell present in the hive but they would only be good at their own "unicorn brand" spells + the spell color coded to them. Meaning a purple could cast invisibility and shield but not as well as a blue or green would. In the same vein a former repair pony could cast a healing spell but not as well as a former doctor. This would have disappeared when the Goddess died as she was the big hub, it would be as if the local internet server suddenly crashed (lots of lonely little computers wondering wtf just happened).
Regarding souls. Souls are resilient bastards and not easy to mess around with, so the spirit of each alicorn was probably still present in their own bodies, just suppressed by the Goddess. The only souls to float free was probably the ponies bodily absorbed by Trixie herself. And these dissipated to whatever afterlife ponies have shortly afterwards.
Anyway that's all I have atm.

Feel free to correct me if you think I am talking out of my ass.