It shouldn't page split due to inserts. As you say, it's an increasing column and new rows will always be at the 'end'. The clustering key will be present, but as an include column (since that's a unique nonclustered index). It might be able to split due to updates through. What's the data type of the clustered index key, can it ever change?
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability