No, in a client like Outlook you can store the login details and passwords for several accounts and set one of them as the default account for sending new messages. Next to the send button is a dropdown menu allowing to to choose a different one, but you have to remember to use it.
To be honest, if (as the Indo says) "it is the first major controversy Mr White has been involved in since taking up office", then it's pretty piddling compared to some of the other ministerial "interventions" that have come to light over the years (across all political parties). At worst, he accidentally on purpose used his position to try to obtain favourable treatment for his daughter on an insignificant issue, the location of her college work placement. He wasn't trying to get a rapist off the hook. And you can be pretty sure that the NUIG Faculty of Medicine knows "who she is" without Daddy having to use his Oireachtas email address.