Yes, NodeXL will work with the 2007 version of Microsoft Home and Student Excel. In fact, the software is configured and developed to work with the following versions of Microsoft Excel: Microsoft Excel 2007, 2010, 2013 and 2016.
As always, for that to happen, you need to download the latest version of the software and the latest updates for the 2007 version to be installed through the Windows Update. This is to avoid any issues that might appear.