No. Please read Paragraph 245ZU of the rules...
All migrants arriving in the UK and wishing to enter as a Tier 4 (General) Student must have a valid entry clearance for entry under this route. If they do not have a valid entry clearance, entry will be refused.
Your sponsor will get into trouble if you attempt to study as a visitor when the course requires a T4. When sponsors get into trouble, they tend to revoke the person's CAS. If the trouble was caused by the student (like in your case), they will not issue another CAS to them. When they sent you the stuff, they advised you (along with the guidance) not to make travel plans until the visa was issued.
Additionally, they will not let a person enrol their biometrics from within the UK as part of a T4 application. That was the whole point of introducing biometrics as an entry clearance requirement. Also, trying to get a T4 from within the UK will lead to a refusal with possible removal instructions and then matters will be worse. Americans are not exempt from these rules.
We can answer here because it's urgent; your follow-up questions should be posted on the Expats site.