Yes, in the message you can instruct a signer to upload an additional document as an attachment, like an ID or bank statement, during the signing process.
You can request uploading an attachment optionally.This means that sometimes signers will forget adding it and you'll need to send a follow up email.
You can however also make it a requirement to upload an attachment to allow finalising the signing process. To add this requirement you can add the name of the attachment you desire in the prepare window as shown below.
Please note that SignRequest can not scan the document to check whether or not the uploaded document is indeed the type of document you requested.