Is it bad practice for SEO to use <i> in header elements?

I would say it wouldn't harm much, nor will it add anything. I prefer to keep my header tags clean and wouldn't add the i. The inline styling would be a bigger problem, which isn't really an big issue.

Instead of doing this, you can add the gear icon to the H2 directly:

h2.Geared:before{
    display: inline-block;
    color: rgb(102, 149, 45); 
    font-family: "FontAwesome";
    content: "\f013"; /*The actual character FontAwesome uses */
}

<h2 class="Geared">This text will have the gear</h2>

Google pays almost no attention to which tags you use these days. Google cares about how the page looks to users. It cares about which text is big. It cares about which text is prominent. It cares about which text is hidden. Recent SEO tests have shown that there is no difference between using a <div> tag that is styled to look like a heading and using a <h1> tag as far as Google is concerned.

I frown on using tags for italics rather than using CSS. It mixes semantics and presentation. However, from an SEO standpoint, there should be no negative or positive consequences.