Hi @Cameron Moody ,
Welcome!
Nope, as I know, “Download headers only” has not been available in Outlook for Android yet.
"Download headers only" is an option that is only available in Outlook desktop client, please check: How to set Outlook to download only E-mail headers. (Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.)
If you have a demand to add this function to Outlook for Android, you could try voting for this thread: add message download option headers only or full message in User voice, Microsoft may notice it and add it in the later version.
By the way, please kindly understand that here we mainly focus on general issues about Outlook desktop client, if you would like to know more information about Outlook for Android, I would suggest you to post a new thread to the dedicated forum for Outlook for Android.
The reason why we recommend posting appropriately is you will get the most qualified pool of respondents, and other partners who read the forums regularly can either share their knowledge or learn from your interaction with us. Thanks for your understanding and hope your issue could be resolved soon.
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