If you a ran a very slow relay, would you be contributing much to the network or would it not help very much?
Every relay is important for the diversity of the network. The anonymity is the direct result of diversity of the network. Diversity of number of relays, diversity of number users, diversity of nature of network usage, diversity of number of directory authorities, etc. Without the diversity you may as well forget about anonymity. One can make a mathematical hypothesis that as the number of relays go toward infinity (read very large number of relays here) the anonymity go toward reality (read going toward perfection here). This is also true about diversity of number of users, diversity of nature of network usage, diversity of number of directory authorities, etc. To put it clearly, The large number of slow relays is much preferable to small number of fast relays in the sense of anonymity. The reason is that more distributed the network is the more difficult it become to totally control and snoop on it. In practical terms one might not be able to reach infinity, but going toward infinity should be the goal (read steadily increasing the number of relays). In other word one can never become perfect but pursuit of perfection should be the goal. When one talks about slow relays, one should understand that slow is a relative term and as I understand it in practical terms Tor advise a minimum bandwidth requirement (250KB in, 250KB out) that relay should provide. This should be enough, to handle the network practically. No additional restriction is necessary or desired.
No, a very slow (whatever that means) relay would not help. No traffic is directed to a relay below a certain bandwidth threshold. Any adversary can disregard all nodes below that threshold when considering which nodes to watch.
Besides, do you really want your traffic to be routed through someones 64KB/sec soda-straw? Yeah, no one else does either.
Very slow relays are nothing more than a feel-good exercise. Spend a few dollars on a VPS and make an actual contribution to the Tor network.
A very slow relay may not be particularly useful for relaying traffic, but it can find other uses in the network such as being a hidden service directory.
Actually, I think that might not be the case... If we were to grow the network to have more fast relays than users, that would most likely harm the anonymity. There would be high probability that each relay would only forward traffic of one or two users at any given time, which would make it easier for an adversary to "spy" on the route that a certain user was building through the network. Of course, we will never grow the network to that point so this is pure theory. However, I think slow is a very subjective notion, so I think for now we should use all relays that are available. I disagree with using the slower ones to hidden services. HS are already slow as it is, and the idea is to make them faster so they get to be more reliable and used by more people. That's why they are being completely redesigned. Improving HS security and speed is essential to protect the freedom of the Tor network, and thus of the internet.
One more thing: while a small number of fast relays might seem as a bad idea, if there are enough users to make it diverse, it becomes harder for an attacer to try and identify a user based on which websites are being visited (thus knowing that relay is being used by person X and so person X visited also that other website). We need to grow the network but also the users.