No, the ID + varchar column will not work. This is great for queries in which you are viewing the identifier, and just select the identifier and / or varchar column - then you will have a coverage index, and everything can be restored only by viewing the index.
I assume that you have a clustered index in the ID column as the primary key. Then you will need to create a non-clustered index in the varchar column, which should be possible. A non-clustered index also automatically includes an identifier.
Also remember that the index will only be useful for queries such as WHERE VarcharColumn = 'xyz' and WHERE VarcharColumn LIKE 'xyz%'.
This will not help for LIKE queries "% xyz%" and "% xyz".
Mark S. Rasmussen
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