A student photographer (if you really look) will bring the benefits of contemporary work which is much sought after atm.
They really know their stuff however there are two things you need to consider.
1) Photography is one thing- wedding photography is another.
Wedding photography is an art within itself and the student will really need to research on this to make sure they are within the loop. There are so many important factors within a wedding and photos that should not be forgotten. Make sure they are aware of what YOU want (inc the style and specific photos- build a portfolio of your fav wedding pictures to show him/her) and also the attitude they have. Weddings are stressful and emotional and they need to be aware of the day and what it means to you- so they'll need to build a client rapor with you to truly respect the day.
2) Reliability. They are not 'wedding photographers' and they are not running a professional buisness and you need to be cautious of this. If you feel like you need to draw up a contract to have peace of mind then thats up to you but they are not 'bound' to provide you a service and you should be aware that if they are ill or unable to attend on the day there is no back up.
On the whole, student photographers are fresh and keen to build their portfolio, they know what will look fantastic- just make sure you understand each other and that you are certain they will be reliable on the day!