From what we have so far, it appears we will need avatars of some sort. A structured graphical conversation requires visually more for people to quickly differentiate between participants than plain text, so just links won't be sufficient. Plain link signatures barely stand out enough to be all that useful even without being surrounded by other formatting and structural elements.
- We should be able to relatively easily test if this actually matters if need be. May not even need flow itself; how hard could it be to tack it onto a LQT somewhere and... something.
Alternately we could just use random pictures of slime mold for everyone and not worry about it.
So many ways this could go horribly wrong
- Penises, Muhammad, creepy hairstyles, anything that could be construed as offensive, intimidating, or otherwise inconducive to a collaborative collegial environment...
- Just plain random images not actually associated with the user - more likely to make people uncomfortable working with them
- Photos of people who are not the user (e.g. celebrities)
- Photos of minors
- Copyvios (anything from non-free content to cc-by lacking attribution)
The policy writers will love this.
- Same avatar cross-project? Different projects tend to have different policies regarding signatures, file usage, etc, so that could be problematic...
- Description pages? Wikia just has avatars as a separate thing entirely from general files and frankly doing otherwise seems pretty silly especially considering how small they tend to be, but we do need to know/verify the copyright status and sources of them same as any other content...
- Even using files off Commons wouldn't necessarily work - avatars are generally expected to link to the user profile/page/feed, not to the file description.
- Possible workaround for at least attribution might be to have source info in a popup, but how do we use/modify that?
- What would IPs use, identicons?
- What sorts of defaults wouldn't be potentially alienating? On enwp the default signature doesn't stand out precisely because it is so widely used by experienced editors and thus it isn't generally a hurdle for new users, but something like that would be a lot more difficult with meaningful avatars...
- "The choice of avatar can significantly impact people's comfort."
- "If members within a virtual team are represented by avatars which are similar to them, it will increase their identifiability within the team. This would make them cautious regarding their behavior and work performance, and, eventually, it would be instrumental in reducing the social loafing that occurs within such teams. In addition, anonymity within a virtual team setting has been linked to lack of trust and accountability. If team members can be easily identified, it will lead to increased credibility and accountability." 
Cultural differences will apply to avatar use and response same as any other dealybobber, but significantly? Nevermind Muhammad pictures here; these are effectively the same sort of thing as an image one might put in a userbox, but carried with them along with all associated implications with regard to interaction...
- Things that have meaning in one culture just plain won't in another - lack of concept, or an expression generally just grouped differently...
Choice of avatar says something about a person - women tend to choose female or non-human, younger folks will choose ones reflective of their demographic, etc.
Many users value anonymity and a picture, arbitrary as it may be, takes that away, reflecting their particular choice on them and lending preconceptions to other participants that they may not otherwise have had because now they see the image and judge based on that before even reading the post/response. Now on one hand a perceived recognisability helps foster trust of others and likelihood of considering them positively (reducing uncertainty makes folks more comfortable, and avatars do that), but on the other the lack of preconceived notions allows folks to step into any given situation without the subsequent expectation constraints.
Folks act according to how they expect others to perceive them - so an avatar will affect that.
There is considerable research on more advanced avatars are are used in 3D environments and gaming.
- An individual's Second Life avatar's appearance will impact their behaviour in-game regardless of personality outside
- Indications that avatars that more accurately represent an individual to themself also do to others and that increases trust, productivity, and civility within a group...
- Me and My Avatar: Exploring Users’ Comfort with Avatars for Workplace Communication
- Impact of similarity between avatar and their users on their perceived identifiability: Evidence from virtual teams in Second Life platform
- The Influence of the Avatar on Online Perceptions of Anthropomorphism, Androgyny, Credibility, Homophily, and Attraction
- The Proteus Effect: How Our Avatar Changes Online Behavior