Yes, the fact that Sanders' delegates will have to pay to attend the Democratic National Convention will hurt turnout by his supporters. Many people are unable to afford to travel and to attend the convention and will be forced to stay home. Some will still attend despite the cost, however.
The need for cash at the Democratic Convection will hurt turnout of Sander's supporters. This is making the campaign to expensive and given the fact Hillary Clinton is poised to be the ultimate winner in the Democratic nomination race, most of Sander's supporters may just decide not to show up.
Most of Bernie Sanders' supporters are not that affluent. However, one must have the money available in order to attend the Democratic National Convention Therefore, it is no surprise that many of his supporters do not have the money to attend the Democratic National Convention. In short, a lack of funds for his supporters will likely hurt their turnout at the convention.
Bernie Sanders supporters are strong ones. Though they may be miffed by the needed cash for the Democratic convention, it is my belief that they will cough up what is needed in order to continue to display their support. After all, what ISN'T cash needed for now is more the question.