The answer to the question, as indicated in your topic, in general is no. Because you usually prefer to have the narrowest (albeit non-clustered) index.
But in your case, you select *, so if the clustered index is good enough for your search criteria, it will always be selected, since something narrower will need to be searched in the bookmark.
So, the big question is, why is this query the way it is, is there a better choice of a clustered index in general for your application (narrow, static, increasing, unique) and whether you really need to be getting all the columns. Because none of the two options you give is truly typical of good design.
500,000 rows are pretty small, but if performance is a problem, you want to see how many rows are suitable for each page, and whether you can improve, which will be more selective in your query and have a covering non-clustered index.
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