No, this dialog is not open to be reached or controlled from MIP.
Something that is open and can be used in MIP plugins is the Alarm Preview as shown in the Smart Client Alarm Preview plugin sample. https://doc.developer.milestonesys.com/html/index.html?base=samples/pluginsamples/alarmpreview/readme.html&tree=tree_1.html I hope you might find that one usable.