Can indexing views in SQL Server 2005+ speed up SELECT count(*) from a View?
Typically you index views if you are often running aggregates, not to magically speed up joins. Also if you are not using table partitioning there is no good reason to investigate partition-aligned indexed views.

You should be focusing on optimizing the query, irrespective of the view, IMHO. An indexed view is not a magic turbo button (though a lot of people seem to think it is).

Also consider whether you should just run a query separately from the view anyway - often people run a lot of queries through the same view for convenience, even if the view actually touches more columns / rows than are necessary for the specific query.