Yes, and no.
You can use shading instead of highlighting. That is permanent formatting.
Instead of just find, use the Replace feature (Ctrl+H).

Put the word or phrase being found in the find box and the same word in the Replace With box but click on the More button and then Formatting > Borders and Shading. Pick a shading color. Replace All.

Do the same with other find targets. If you want to clean this up you can try to find that shade (with no text) and replace with no shade and no text.