Hi @Andy ,
Yes, SharePoint online sites can be opened by SharePoint Designer 2013.
1.Open SharePoint Designer 2013 > Open Site
2.type your site url > Open
And to make SharePoint Designer work for SharePoint Online, please download and install the following updates in order:
Download and Install SharePoint Designer 2013
Download and install SharePoint Designer SP1
Install 2016 Ang(8) update
For Reference: How to install SharePoint Designer for connecting to SharePoint Online
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