You will see that setting the line-height at 1em is asking for trouble. You could get away with it for 8 or 10 lines but then the drift sets in, especially in IE. You may find other browsers a bit iffy too. To my eyes it looks bad anyway, even when the lines are not drifting. It is just too cramped. But perhaps it has a use for small paragraphs.

As a general rule, the longer the paragraph size, the larger the line-height should be to be safe and to look right.

As it is likely that resizable underlines will be used primarily just for display effects, and not for everyday use on a variety of paragraph sizes, a little experimentation will not go amiss. Just set a different line-height then adjust the image height accordingly and you should soon find a setting that suits your needs.