Yes, the workflow of course is the important piece but there are two options for having someone add/update recipients to the envelopes workflow. The two options are "Specify Recipients" and "Update Recipients". Basically, they both allow additional signers to be added/updated as well as adding private message, viewing the document, etc. In your scenario, you could do this multiple ways. Set User A as a signer and also as the next person in the flow to add additional recipients/signers. Or set User A as just the person who specifies/updates recipients and they add whomever is required to sign, adding themselves if needed.
Now if you are asking if User A is set as a Signer (but not set as Specify or Update recipients) the only option is to "Assign to Someone Else" which basically removes them as a Signer and puts them in a Carbon Copy role instead.
Here is how these Recipient types breakdown...https://support.docusign.com/en/guides/ndse-user-guide-add-recipients
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