Probably not, but it would be impossible to say since you provided neither
your Outlook version nor your fax version.

Sure, have the recipient email you stating they got your Fax.  Pretend you
have a dedicated Fax machine; you receive the same confirmation from the
destination on your PC as you would if you had dedicated Fax machine
instead.  Since a Fax machine knows nothing about email, about the only
email confirmation available would be if you included instructions to the
Fax recipient that he/she email you one.

Hal