MySql - Global index
You would not be able to partition that table as you need to remove the unique key and make it a regular index instead.

To answer your question, if you query on column that isn't partitioned then MySQL would query every partition one-by-one until it answers the query.
So if you query a partitioned table on a column that it is not partitioned on, you may get slower results then if the table was not partitioned.

That is why you need to choose the column you want to partition very carefully.

I would select a column that fits 80% of the most important use cases.