Can the customer I am sending attach a requested document as part of the DocuSign process?

Yes, when in the tag or field portion of the envelope creation process, if enabled, you can add an Attachment tag/field to the envelope document. This allows the Recipient (that it is color coded to) to add an additional document to the envelope. Here is a DocuSign article that shows the attachment field....

https://support.docusign.com/en/guides/signer-guide-signing-adding-attachments-new

Note: Allowing a Sender to use the attchment tag is a global account setting as defined under the Admin > Sending Settings. The setting is called "Enable signer attachment field". Here is another article if this is not enabled...

https://support.docusign.com/en/guides/ndse-admin-guide-sending-settings