FK on NON Primary Keys
Two things:

1 - You still need to have a UNIQUE constraint to use a field as a foreign key.

2 - In your example you WILL have a performance decrease, because by default a PK is also a clustered index.  A non-clustered index on your FK field will speed the JOIN but you will still need to pay the cost for a bookmark lookup since the other fields aren't at the leaf level of the index.  If you INCLUDE(otherdata) in your NC index then it should work fine (assuming that ID is your clustered index.