Only if you sign in to Message+ app with that phone number's profile login. And then if you're using the Desktop Message+app, all the messages may not be sync'ed completely as being reported in numerous currently active threads in this Forum.
Being in control of the account is something that crosses my mind too. jav6 is correct. You will have to log in with their Verizon Message login info in order to access their information. To better understand your inquiry, what is the purpose of accessing this information? If you are looking to limit or monitor the texting you can learn more about our Smart Family app here: http://spr.ly/6608ENE90