The signing itself takes place within DocuSign. Initiating the signature happens within Web Access, and you can configure the DocuSign Endpoint to bring documents that have been signed in DocuSign into the repository.
As such, while a user needs a Laserfiche license to initiate the process from within Web Access, they do not need a license to perform the signature in DocuSign.
Regarding mobile accessibility: I believe DocuSign has support for signing on mobile devices, so this should be possible. I do not think Laserfiche Mobile has support for initiating the signatures.