Yes. Here are a couple of ways to view a Spotify user’s public profile:
Once you are viewing a user’s public profile you can add the user to your People list by clicking the “Add ..” button at the top of the page.
Just want to make another note after sending some of you direct emails.
Usernames are just one word or a series of numbers. You won't be able to search for just 'John Doe'. If your friend goes to his/her Overview Page he/she can find the right username.
Then search 'spotify:user:(his username)'. You'll then find the profile. https://www.spotify.com/account/overview/