How much are relationships/indications of interest helpful to program admissions?

[fakecoffeesnob]

I'm applying to a comatriculation program at a grad school connected to my undergrad institution (current junior) - unfortunately, due to a few poor math grades, I'm a long-shot candidate.

I've been in touch with one of the program administrators, and I got permission to take one of the core classes (a pretty quant-heavy class, that could hopefully offset some of my math grade issues) of the program as one of my standard undergraduate classes, without program admission or any of that. I'll be taking that in the spring. I'm very aware that it's essential that I do very, very well in this in order for it to help my admission chances.

I have the option of applying in the spring or in the fall. If I applied in the spring, I could start taking grad classes in the fall, which would be nice since I'll basically be done with my undergraduate requirements this spring and plan to graduate next winter if at all possible (and if I did this, the cost of undergrad+grad tuition would be the same as four years of undergrad tuition, meaning I wouldn't be particularly concerned about funding). Plus, spring admission might mean that I could graduate on the typical four-year timeline, but with both degrees.

Is it worth it to wait for the fall application deadline, though, so that I will have been able to build a relationship with the department before that through that class? Would this be a situation where applying twice might be acceptable if spring didn't work out? When should I apply, and is this indication of interest likely to aid my application much?

Spring application also precludes taking more time to study for the GRE (although I'm actually feeling okay about that) and building more work experience over one additional summer - what I have is pretty good, but I'm also 20, so I don't have much (and virtually nothing in the way of research - I'm hoping that the fact that this is very uncommon at my institution for undergraduates to do in the social sciences will compensate for that. I should have, and I'm trying to see if there's a chance I can swing that with two particular professors, but unfortunately, I don't think I'm going to have much. I tend to assume they'll be more understanding about that the more junior I am but I don't know).

Any/all advice is welcome. Thank you guys so much!

Edited December 17, 2013 by fakecoffeesnob