Hi,
not natively, but you can do this with a simple plugin, follow these steps:
1. Create a field for modified date (text or date type)
2. Build plugin to do this base on our skeleton plugin:
- Download, install and enabled skeleton plugin (you will find at http://docs.easy-profile.com/index.php/article/triggers)
- Open file /plugins/jsn/skeleton/skeleton.php
- Remove samples functions: triggerFieldAvatarUpdate, triggerProfileUpdate
- Create a function to do this like:

public function triggerProfileUpdate($user,&$data,$changed,$isNew){

		$data['alias_of_modified_field']=date("Y-m-d H:i:s");

	}

this code store in field "alias_of_modified_field" last edit profile date, in this example we use SQL format (Y-m-d H:i:s)

You can hide this field in frontend (no profile,no registration,no edit profile page), so you will see only on backend.

NOTE: this code is not tested and not supported