Applying for UK Visa from USA (CA)

Your document checklist doesn't need a signature when you apply from the USA, and you don't even need to include it with your visa application at all. You may still receive a visa, as this person did.

There is a special process for applying for a UK visa in the USA. Unlike in many other countries, there is no appointment to visit to a VFS office to submit your documents and have them checked. (The biometrics appointment only takes biometrics and handles nothing else with respect to your visa application. They cannot even look at your visa documents.)

If the only thing you've forgotten is the signature on the document checklist, then you do not need to worry. Your visa will not be refused because the signature -- or the checklist! -- was missing. If you forgot other important documents, such as your bank statements, then you may want to withdraw your application and reapply.