EBS will use the estimation history of the last person to estimate the case to generate probable hours to completion for the case. However, the 'up for grabs' user is considered to be the user doing the work, so EBS will assume that all of the work will be performed serially. So the burn-down charts will look correct, but the other EBS projection charts will be off because they attempt to parallelize and get calendar dates.
So if you want to do Scrum burn-down style analysis on EBS-adjusted hours, you're fine as you are, but if you want calendar-date predictions and dependency analysis, you need to assign the cases to the people who will be performing the work. Future iterations of EBS may try to support calendar-date prediction for this setup, but it would require some new notions, such as what is the team for this sprint, can they all work on any case, etc.