"Maybe". Starting with XE16, the menuItems[].action
attribute for TimelineItem can take the string GET_MEDIA_INPUT
as a setting. This seems to be intended to let people record other media from the voice prompt screen if they select the menu item.
The documentation says that transcribed text is the only thing currently returned, but this may be what the Hangouts app is using to let you to take a photo and share it as part of the menu action. You may want to try this out to see if it works yet.
You would still need to do the sharing on your end - The Mirror API doesn't handle any cross-user interaction itself, just lets you know who the user is replying to. You would do the reply in the way that makes sense for your system.