Is it possible to make little Character Portraits appear next to text boxes?

From OHRRPGCE-Wiki

Using actual textboxes, nope. However, it might happen in the future, particularly after QBasic is dropped.

However, through some plotscripting, fake textbox faces can be achieved. Faces by Serg is a tech demo showcasing his plotscript which uses NPCs to create the textbox backdrops.