Try passing the class name to remoteLink, which creates a link that uses Ajax to call a remote function and you can add your fontAwesome classes to it.
<g:remoteLink class="btn icon-ok" action="index" >
click (without i tag)
</g:remoteLink>
or
<g:remoteLink action="index" >
<i class="btn icon-ok">click (with i tag) </i>
</g:remoteLink>
Both approaches should work.