Very often, text in browsers does look ugly. Surprisingly, IE/Edge do a pretty good job smoothing font with Cleartype. For other browsers, I make good experiences with font-smoothing. So yes, take a look at the result, do some A/B testing and then decide wheter you like it or not :)
For reference, here is my smoothing CSS. It tries to smooth the font even when font-smoothing is not available (via text-shadow).
-webkit-font-smoothing: antialiased !important;
-moz-osx-font-smoothing: grayscale !important;
text-shadow: 1px 1px 1px rgba(0,0,0,0.004);
-webkit-text-stroke: 1px transparent;
I prepared a simple comparison for you: jsFiddle