How important is full-text search to the organization's business?  Can they wait for the indexes to be rebuilt?  Some people use search heavily while others don't, so if you want to justify not backing them up on a cost-benefit basis you'll really have to be familiar with their usage patterns and what efficiencies they gain from the system.

If the organization has a formal disaster recovery plan it probably specifies the amount of time by which all systems must be returned to full functionality.  In that case, you'll probably lean towards backing them up unless you're sure that indexing can be completed in the allowed time. Remember that indexing time increases as the repository gets bigger, so even if you think you have enough time today you still have to revisit this question periodically to make sure your decision is still the right one.