What problems would this implementing this feature really fix? The occasional gif in chat happens too infrequently in chat to disrupt the general flow of discussions in most chat rooms. Even if it happened en masse, one could always flag it as spam or for moderator attention, if such an action is merited.
How would it affect the general flow of things?
Depending on how you like to utilize chat, adding this feature might be disruptive to the one's general flow of things. If I often like to idle in an particular chat on one screen while I'm at work (or at home playing a game on one screen), I'll occasionally glance at it to follow the conversations. Adding such a feature would force another added level of effort of moving my mouse all the way to the chat window and click just to play a GIF, taking away from time I be doing other things (procrastination included).
Depending on how it's implemented, the click-to-start, click-to-stop behavior would be a bit disruptive. If I wanted to save the particular GIF at it's original resolution (either because it's awesome or because I foresee a need in the future to use said GIF). At the very least, if this feature were to be implemented, there needs to be a quick and easy way to view and save the original GIF.
Would it really affect bandwidth?
As for being more bandwidth-friendly, (again depending on the implementation) loading both the still preview image and the the full GIF would still be required if I intended to view it. I also don't see occasional GIFs as a huge bandwidth problem, especially since the largest ones that can be uploaded using the chat upload interface are restricted to be <= 2MB (and most are far smaller than that anyway). Typically, GIFs are infrequently used by most users, if it becomes a problem, that's what chat flags are for. I can see a potential need for implement with mobile users who typically have monthly data limits, but it shouldn't matter much to most people on desktop clients.
Would it be user-friendly?
I'm not convinced that being required to click an image just to play the animation qualifies as more user-friendly (it works better with videos due to their length and file size). Especially if the discussion in a particular chat is moving quickly, the likelihood that it would have already been bumped up by the by the time I get my mouse up to that screen is pretty high. If it becomes a problem, especially in highly traffic chatroom, one could always coordinate with the moderators of that particular community and give room ownership with trust worthy regulars so they can help move or delete disruptive or inappropriate GIFs.