Text box, or no text box, that depends:

[Alte]

From the perspective without having a text box,
The texts should be able to support itself if they have outlines.
Which make them resemble to subtitles.

There's articles on: How to do subtitles well – basics and good practices and Increasing Game Accessibility, Comprehension at Gamasutra that could help with understanding of its usage.

The screenshots below are examples of visual novels from Steam where the text box are semi-transparent (hardly noticeable) or invisible. (none at all)

fault milestone one - ALICE IN DISSONANCE | Sunrider: Mask of Arcadius - Love in Space

An Octave Higher - Kidalang | Asphyxia - ebi-hime | Brilliant Shadows - Ithaqua Labs

This can be done in Ren'Py.

Wanted to mention that it's possible for text to have outlines.

This way the text will be readable, even if the font colour is similar to the background, if you are using a semi-transparent or invisible text box.

How this could be used
The nuts and bolts

Thinking without the box.

[Tyrantauranox]

I don't have a strong preference, unless the text box is seriously getting in the way

[KnotUntied]

It may not fit in some genres, but it's certainly a nice addition to a visual novel.

[jQ_theeNHK]

Thanks for posting this! I like the look better without the text box!

Cheers!