It's nuanced, but you can use techniques like app URL scheme querying to determine what is installed. [1] People will be replying to you with information from 2011—today, it is generally not possible to query for a large number of installed apps this way. So generally, the answer is no.

Without going into much detail, the state of the art uses Facebook in a peculiar way to determine which _relevant_ apps are installed, relevant meaning high grossing (Clash of Clans, Spotify, Tinder are examples).

[1] http://useyourloaf.com/blog/querying-url-schemes-with-canope...

They're allowed to ask "does anything on this system handle yelp:// URLs?".