Using a Logo in the Header

Do all Omeka Classic Themes allow the use of a Logo?

Even though this was originally posed in the Omeka S Theme category, you seem to be asking about Omeka Classic. All themes for Omeka Classic developed by the Omeka Team allow for the inclusion of a logo. Please review the documentation: https://omeka.org/classic/docs/Admin/Appearance/Themes/#configuring-a-theme