Is it an antipattern to have a consulting firm provide both the coach and developers?  By providing the developers, the firm is motivated to deliver on the project, with coaching as an adjunct.  If, instead, the firm provides just the coach, it will be judged by how well the client adopts the process.  These two motives can easily conflict.

Case in point: at a previous client of mine, my employer was charged with completing the project, using a 50-50 mix of contractors and client developers.  My employer, a consulting firm, provided several developers experienced with XP and Scrum, as well as an agile coach.  The firm was thus charged with two imperatives: first, deliver the project; second, introduce agile methods within the client. 

With project success as a requirement, the firm decided to intereview the developers at the outset of the project. The client's developers (rightly) perceived that they were interviewing for their own jobs.  This started a negative dynamic that ultimately resulted in 80% attrition among the client's developers.

On a pure coaching engagement, the coach would probably have "made do" with whomever the client provided. 

We delivered all the features, basically on time, with very high quality. Financially speaking, it was a success, generating more orders and more revenue per order than its predecessor.  It is harder to say that the engagement as a whole was a success, though.  Almost all of the developers were contractors, so the client got their product, but very little adoption of agile methods.

Perhaps if the coach and the contract developers had come from different firms, the motivations would not have been as tangled, and more of the client's valuable people would have stayed.  The team might not have suffered from the strained, unhealthy environment from the early days of the project.

Then again, perhaps not.  The client may have been expecting that level of attrition. Maybe that's just to be expected when you trying to bring a random selection of corporate developers over to agile methods, especially if the methods are decreed from above instead of brought upward by grass-roots. Maybe the dynamic would have existed even with a coach that was totally disinterested in the project outcome.