I don’t think so.
I think No matter how many category you have, wordpress run only 1 query to find category name in category But only 1 thing is if you have so many category so it might use more time to find but still use only 1 query
But I don’t think the time to search is problem because 1000 category = 1000 table row in database and it very fast to search. It will finished in millisecond
Actually wordpress work like this =
Query > wp_term_taxonomy – to define category or tag (or custom tag or custom post type – if you have one) and then
> wp_terms – to find category name example “yellow shoes”
> if you have 1000 category – it will search through your database row in wp_terms table
all above use only one query
From my personal experience I have many wordpress websites and install wordpress many times, I found that default wordpress setup use a little bit resource and database query (around 20-30 queries) If you just use wordpress as normal (no plugin + use default theme) so nothing to worry but other extra things will add more query to database example plugins or custom theme or extra function that not properly coding
example I had ever try to write my own function to show 10 recent posts in sidebar with show image in post too. this function eat many query because my code request database query every 1 image in 1 post and another some small function that also use query . when i put everything custom recent post + custom recent comment + custom related post = 200-300 queries from normal at 30-50 queries
Can you tell your website address? so we may help you to see what is your really problem and you can try blow plugin to test and see your site
Try this plugin http://wordpress.org/extend/plugins/debug-queries/ before and after you enable WP No Category Base
Debug Queries will show you how many query wordpress run and which query they require to run
