Was Does Sought After Mean?

: wanted by many people and hard to get or find sought-after antiques the most sought-after artists.

Are much sought after?

In demand; very popular with or desired by a lot of people. To the surprise of some, the product has been greatly sought after since it was first released.

Is sought after correct grammar?

"Sought-after" is idiomatic usage for something that is desired. Dictionary.com: Idioms 9. be sought after, to be desired or in demand: Graduates in the physical sciences are most sought after by employers these days.