If you know that the constraints on each of the tables is distinct, then building a UNIQUE index on each of the partitions is sufficient to prove that all rows in the combined partitioned table are distinct also.
The hard part there is checking that the partition constraints are distinct. If the partition constraints are added one at a time, you can use the predicate testing logic to compare the to-be-added partition's constraint against each of the already added constraints. That becomes an O(N) problem.
What is really needed is a data structure that allows range partitions to be accessed more efficiently. This could make adding partitions and deciding in which partition a specific value goes an O(logN) operation.
If the unique constraint is supposed to be on a column which is NOT being used for the partitioning, then all the above becomes much more difficult. While partitioning, the additional onus on the user is to specify non-conflicting CHECKs for the range/list partitions.