Depends how you define "design". Most engineers I know are not involved in the bog-standard design, but rather when the decisions get outside the comfort zone of the designers (either engineers or engineering techs themselves). From all accounts ("Switching to stainless steel is one of the best design decisions I've ever made"[1], comments from Tom Mueller about Elon leading the design team on Raptor[2]), Musk is performing the role of a head engineer.
Many jurisdictions would still have an issue with him using the title engineer. (edit: it's recently been determined to infringe on first amendment rights [3]. Still applies in Canada)
[1] https://www.youtube.com/watch?v=P06X2TZUKZU&list=PLpEqMkxe7X... (From the "Dan Rasky: SpaceX's Collaborative Design Approach" video of the "COTS: Dan Rasky" playlist of "Knowledge @ NASA".)