How does MySQL or PostgreSQL deal with multi-column indexes in ActiveRecord?

I’m creating indexes for my models right now and I want to know how MySQL and PostgreSQL deal with an index with more than 1 column like:

add_index :users, [:username, :created_at]

That should utilize the index when I do a query like (I think):

User.where("username = ? and created_at > ?", 'jim', DateTime.now.yesterday)

But will it also utilize the index if I only use the username in a query?

User.where("username = ?", 'jim')