I’ve directly opened an attached Word document, did some editing and then saved it, without using "Save as" to select a folder. I have no idea where I have saved it now.
Is it still possible to recover the edited file (the document)?
When you directly open an attachment from within Outlook, the attachment is copied to and opened from a Temp folder.
Recovering files from this Temp folder (also known as OutlookSecureTempFolder) is not a one step process and is different for everyone.
You can find full details on how to locate and open this folder in this guide.
Note: To edit an attachment and make Outlook save the changes to the original message rather than saving the modified attachment outside of Outlook see: Save attachment changes with original message