Unfortunately this ticket is only valid between the four stations en route. A ticket such as Box Hill & Westhumble - Redhill would have been a similar price and valid for the complete journey Leatherhead - Dorking - Redhill - Coulsdon South.
Seriously?? How can a BHW to Redhill cover me to Coulsdon South? It's two stations beyond that? :/
It's a little more expensive, but could well be well worth it for you. Your ticket is £29.40/week while the BHW-RDH one is £31.60/week. While the logical way to do the journey is Box Hill -> Dorking -> Redhill it is also equally valid via Epsom, West Croydon, Selhurst/Norwood Junction and East Croydon. Thus to get to college you are making two part journeys (Reigate to Redhill then Redhill to Coulsdon South) while to get to work it's a different two part journeys* (Reigate to Box Hill then Box Hill to Leatherhead). It would also be valid to go shopping in Croydon, and if you want to go to London then you only need to pay from Selhurst or Norwood Junction. Not bad for £2.20 a week extra!
*The small print. It is not 100% clear whether the season ticket is valid on a train that doesn't call at whichever of origin or destination that you are going through. That won't be a problem at Redhill, but for a hassle free journey you might want to ensure that your Dorking to Leatherhead train stops at Box Hill. Having said that, there is a line of thinking which says that it is fine on a fast train, and at least one TOC has confirmed this. You may wish to describe your exact situation in a letter to Southern and see what they say.