So here’s an update to my findings with the help of Trasochi from Discord.
The Putrid Wraiths are summonable but they visually appear as Flame Wraiths. If you test this on the target dummy, you will notice the FLame Wraith actuially shoot green poison projectiles but the skin/texture of the model will appear as a Flame Wraith.
Flame Wraiths (the real ones) work as intended.
I did run into another bug (fixed by relogging) where resummoning Wraiths was only ever replacing one Wraith. I had 2 wraiths, one Putrid and one Flame. I was supposed to have two Flame Wraiths but the Putrid Wraith was obviously bugged and would not unsummon or be replaced. Again, I reglogged and this fixed itself.
I had one more bug where I had a Putrid Wraith (remember, it looks like a Flame Wraith) and it was attacking with no projectiles at all.