I like the idea, I personally prefer red wavy lines for spelling issues (as in pretty much every spelling I used/know, from oses to softwares) rather than dashed lines (that I associate to hints/acronyms rather than spelling).
About the dark background part of your question, I think the current version is contrasting enough (see screenshots below), but of course it’ll depend on the general tint of the ui and its general contrast (the more the base ui is using contrasted color the less your red will have visual impact).
On a side node, after install I noticed that the dashed-line wasn’t cleared:
A couple of tweaks (removing the border and adding some margin), and this is what I get:
Now if there is a graphical improvement that can be done, it’s to smooth the lines a bit to make it more coherent with the text above.