Hi @esstein788 ...
No, this is not possible (as far as I know). The Canvas Inbox is not technically the same as regular e-mail. It is a messaging system through Canvas in which instructors and students can message each other as long as they are in the same course. For instance, a student cannot send a message to a family member or friend via the Canvas Inbox because that family member/friend is not taking the same course as the student. Similarly, a friend/family member cannot e-mail the student and expect that the student will receive that message via his/her Canvas Inbox. The Canvas Inbox is really meant for communication among instructors and students as long as they are enrolled in the same course(s).
Pearson is a third-party integration with Canvas, and even though you might be accessing some Pearson screens through Canvas, the interface systems are completely different. I've not used Pearson much recently (I did a little bit in my former Canvas admin position, but it's been a few years now), so I can't really speak to what Pearson offers for a messaging system. However, I'm pretty confident that you wouldn't be able to receive messages like you were hoping to get via the Canvas Inbox.
Sorry I don't have better news for you, but I hope this helps in some way to answer your question.