Yes, something similar is possible.
Set in the feature editing template the Default Tool to Rectangle
You can accomplish this within an edit session. You just need to close the line or polygon after creating the 3rd vertex.
Introduction to the Editing Tutorial (Version 10.3.X)
Editing Geodatabases Tutorial (9.3.X)
http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?TopicName=Editing_Geodatabases_Tutorial
Don't expect equivalent functionality between different software packages. Tools are developed based upon demand, perhaps creating rectangles from 3 points is low on the list.
Yes, something similar is possible.
Set in the feature editing template the Default Tool to Rectangle