An important thing to consider for Agile projects is that users need to be senior enough to be able to look beyond local agendas at broader business benefit.
Furthermore, the BA can be the one to add that broad view, but can't replace the senior user, as unless they have worked in the role they can't really know it. Additionally the business unit hasn't ‘bought in’ to the new system if done by proxy through a BA. The business definitely needs to send in their user/s.
We had a short discussion about this topic at Better Projects a while back and the consensus was that a BA can't replace the business representative on an Agile project – mainly for the above reasons.
In fact, on Agile projects the developers are expected to do the analysis in an agile project. That’s why they require A-grade team members and work best in less complex business environments.
Potentially a Business Analyst can participate in the team to add depth and skill to the analysis. Certainly they could be working on the next (or future) iterations while the development team are busy building this round.
Another alternative is that the skills of the business analyst are adopted by Agile developers. Teaching Agile development teams the disciplines of business analysis will help them accommodate more complex business environments and deliver more consistent results and in the end better projects.