Rob,
it really depends on the brand/model of the remotes you are using.
Pocketwizards have a significant range, and certainly enough to have a remote camera behind the goal at the other end of a football pitch, assuming you have nothing significant blocking your transmission to it.
I can't speak for the cheaper Chinese remotes although I once did a job with cheap remotes and failed to get a good reliable trigger from about 100ft away and so it could be an issue.
Either way you'd want to be sure you had a unique channel to ensure that you were tripping the shutter on it and not someone else ! Impossible to sort out mid-match. If you don't already have something then that might push you towards the Pocketwizard Multimax with a custom channel - depending on the number of remotes/photographers you typically encounter at a match.
From a logistical point of view you also need to think about being so far away from it from a security point of view and if you are able to get to it at say half-time to gain access to the card to be able to wire, and then there is the issue of how you trigger that remote camera.
Typically on a near goal remote you'll be shooting the action with a body and 70-200mm combination with the trigger on it - you'll get some/quite a few images which you'll just discard because there is no action but because you are predominately shooting goalmouth action only with it you'll get some with the ball in frame even if they are not perfect.
With the remote at the other end you really have two choices - stick the trigger on the body with the long lens (300/400mm) on it - which will result in a massive amount of empty frames as you shoot mid pitch action far away from the far goal-mouth OR trigger it separately on foot-pedal/by hand whilst shooting with the long lens to only get frames when there is goal mouth action you are interested in.
HTH
