I applied late and was only made an offer last week. I accepted, and sent a note saying that I wanted to get a CAS as soon as possible since the visa deadline was fast approaching. I think because of the timing, they sent me a CAS very soon after I inquired despite not having sent them my passport or made a deposit. Hopefully the UKBA doesn't think my application is shady since it shows that I have not paid a deposit.
The EUCLID portal CAS notification says that it isn't necessary to send the CAS allocation e-mail, but I sent it along just because it made me feel a little better.