Are there any issues with sparsely populated partitioned tables The partitioning strategy used by a third party product results in a fairly sparse distribution of data.
i.e. of our ~900 partitions only ~300 have data. The way this works it will only become more sparse over time.
Is there any value in merging consecutive empty partitions (I can guarantee there will be no inserts into them) or is this a waste of time?
Each partition is essentially a separate table, so there is some cost involved in query optimization, statistics, and metadata management.  So if the third-party product supports you removing partition boundary points they created, I would probably do it.

See


  The new, higher limit of 15,000 partitions affects memory, partitioned
  index operations, DBCC commands, and queries. This section describes
  the performance implications of increasing the number of partitions
  above 1,000 and provides workarounds as needed.


Partitioned Tables and Indexes - Performance Guidelines