By putting an image on every page you visit, there is more to load and will drastically slow down the forum load time. To this date, the forum can be loaded within a few seconds even when you have a very slow Internet connection. (Edge(E) cconnection on mobiles).
But if the logo is also plain text or bbcode, it won't make much difference.
Let's see if the new forum software features a logo
And how about user's avatars? They are problem too? Because almost everyone here is having avatar and I don't see any problem with that.
Forum's logo shouldn't be much larger than an avatar in the first place. From technical point of view having logo at top of the site is a not hindrance at all.
I feel that the real problem is designing it.