The UserManager - arcgis.gis module — arcgis 1.8.0 documentation documentation points users to the REST API documentation for search parameters:
Note
A few things that will be helpful to know.
The query syntax has quite a few features that can’t be adequately described here. The query syntax is available in ArcGIS help. A short version of that URL is http://bitly.com/1fJ8q31.
Searching without specifying a query parameter returns a list of all users in your organization.
Most of the time when searching users you want to search within your organization in ArcGIS Online or within your Portal. As a convenience, the method automatically appends your organization id to the query by default. If you don’t want the API to append to your query set outside_org to True. If you use this feature with an OR clause such as field=x or field=y you should put this into parenthesis when using outside_org.
For your specific situation, there is no case-insensitive or wildcard search for AGOL/Portal user e-mails. There have been, and still are, enhancement requests for such functionality, but Esri hasn't acted on them in years. Honestly, I don't think they ever will, especially for wildcards.
Although you cannot do a case-insensitive user e-mail search directly, there is an interesting behavior where you can query on the user part of an e-mail address and a case insensitive search is done. In your example, searching on "First.Last" would return first.last@joe.com; however, it might return additional results as well so you might need additional filtering.
You can also search on company e-mail, "joe.com", since that is likely to be all lowercase, and then use Python to search for the user within that company.
