Not really.
I am actually studying Television Production. The good from it is the guest lectures and the networking events, and I also had the opportunity to be Pilgrim of the Day on Deal or No Deal thanks to a trip there. You get to make films a lot, and you get to unleash your creativity. The truth though is that employers are not going to look at your showreel when you apply for a runners job. On the other hand you can learn some good skills such as editing, but what is stopping you from getting your own camera and making your own films?
However networking is the key in the industry, sadly it's who you know not what you know. I come from a background with knowing nobody in the industry and living in a rural area with poor job prospects. How I started in the TV industry? It was with 4Talent two days after completing my GCSEs. It was my first taster of networking. Then I went to The Unusual Suspects event at Channel 4 who also invited talent managers from BBC and ITV. There were people who had got in through apprenticeships. Employers don't look at your education, they are looking for experience and who you are as a person. I then went on to a placement at ITV Leeds last summer which was absolutely fantastic. I learnt so much in just a space of a week.
This was before I even started university, so it goes to show that a degree is not really needed. It is about getting yourself out there and applying to work from the bottom up. It's hard work at first, but once your foot is in the door it is easier from there. First port of call should be Facebook/Twitter, plenty of jobs going there!
I'm not saying you should not get a degree though, it can show your level of education. But this can be any degree from economics to law.