Suppose there is a table with a compound primary key and said key is clustered.
When I insert a record, I'm taking an educated guess that because of the clustered index, the actual table is re-ordered in some manner if a new record falls between other records.

And yes, that's generally correct. Now, you can set the FILL FACTOR to reduce how frequently page splits occur. If you set a value of 80 (and this is from MSDN), that means 20% of the data page is left empty, to allow/reserve for space that would otherwise cause a page split. I've read different reports on how effective this can be. So mileage will definitely vary based on the usage.