My view would be, why deprive yourself of a chance, however small it may be? I sent out pre-completion letters, not only to give me a chance to be put on the map, but also i wrote to ask advice. It was surprising how many replies I received, and those letters are on file, here, just incase I may need some contacts in the future.
If you aren't sending out CVs, you can bet someone else is, and so much about getting your first firm step on the career ladder, relies on luck and being in the right place at the right time.
Rgds
RB311