If custom post types use the same capability type ‘post’, ‘Yes’, role may have access to all CPT with ‘edit_posts’ or to none of them.
But if every CPT uses own unique capability type then videos will be protected by ‘edit_videos’, ‘books’ – by ‘edit_books’, etc. You can grant access to the selected CPT at the role level in this case.
If you define CPT yourself via PHP or plugin, like “Custom Post Types User Interface” then use unique capability type for this purpose.
If CPT is defined by external source (theme or plugin) you can use “Force custom post types to use their own capabilities” option at “Settings->User Role Editor->Additional Modules” tab. Take into account that this option is applied to all existing custom post types, including WordPress built-in ‘attachments’. Correspondent roles modification would be required.