Grad Schemes: apply ASAP or wait for campus events?

Graduate programmes are open for applications, the CVs are flooding in, recruitment teams are drowning in a sea of cover letters, it's all systems go.
Stop, put down the mouse, don't bother with any more tweaks to your CV, let the timer on the logical reasoning test you're doing make its way to zero.
There are no more seats at the new analyst table for 2017. You're already too late.

I hope not.

Given that:

1) Many (...all) firms encourage you to apply AS SOON AS YOU CAN since recruitment is done on a rolling basis, and
2) they start accepting applications well before the start of the academic year, and
3) you haven't already had the opportunity/ability to get some quality networking under your belt in the previous academic year...

Is it better to:

attain some recruitment alpha by beating the herd and start sending your applications out as soon as you can?


wait a few weeks (perhaps months) so you can attend employer events, career fairs, etc. so you can get out there, meet some employers face to face, and perhaps create that one golden connection which might just make the difference in the whole recruitment process?

The question could be phrased another way: How important are these events? Does attendance really make a huge difference?

Thanks all!