RESOURCE_SEMAPHORE_QUERY_COMPILER waits in Microsoft SQL Server 2008 Enterprise
Could fragmented indexes on Microsoft SQL Server 2008 Enterprise cause RESOURCE_SEMAPHORE_QUERY_COMPILER waits?


No. At least not directly, and even indirectly is not fragmentation but could be outdated stats at play (which rebuilding index also fixes). Read Plan Caching and Recompilation in SQL Server 2012, even though is 2012 a lot of it applies to 2008 still. The problem is that your plans are not reused and you suffer from high re-compilations. Read the white-paper, it has tonnes of resources and explains a lot.