That heavily depends on your definition of "positive impact". In design/typesetting theory there are different "kinds of reading" and some fonts have positive effects, as in "works well with that kind of reading", while others are not very well suited for a specific task.

For example letters with very distinct shapes and different heights between lower and uppercase letters, like often found in serif fonts, are generally said to be easier to process for your eyes and brain.

Your brain learns to "read without reading" by scanning for known shapes and groups of shapes and just recognizing letters and words by that. You start to skip words, letters, whatever, once your brain has internalized that font.

That effect helps with reading faster and with less "stress" which is ideal for longer texts like in a book. Combine that with a good mixture of line length, font size and line height and you can create long texts that can be read very well.

Now take the same font, set it really tiny because you're working on an Encyclopaedia and don't want it to have 300 pages more and those font features that helped you before, actually make it more difficult to read.

Fine shapes might break away in the printing process or run up and your text will be harder to read. A sans-serif font might be better suited here. Straight crisp lines, that can be reproduced very well might actually make a better job here.

So... Fonts can have a positive impact on reading, depending on your definition of impact. ;-)