Yes, a person with a previous version of Microsoft Office can easily open documents created with the latest release of Office.
Office 2007, Office 2010, Office 365, or Office 2013 users can open documents created using the latest release of Office applications without any additional action. Customers using earlier versions of Office may need to download and install a compatibility pack. Microsoft Office Compatibility Pack for Word, Excel, and PowerPoint File Formats
Callstack: at (Apps/Microsoft/Microsoft_Office_2013/Office_2013_FAQ/Can_people_with_another_Office_version_open_documents_I_create_with_the_Office_2013_application?), /content/body/div/pre, line 1, column 1