It's possible, but I think you're really pushing the limits/purpose of TBS. Using your own markup could greatly simplify the DIV-soup that is required to make this work in TBS.
UPDATE: See below for replications of this solution that I've made using Twitter Bootstrap 3. The original question and answer were for Bootstrap 2.
Fiddle Example
<div class="container">
<div class="navbar">
<div class="navbar-inner">
<img src="http://placehold.it/70x70" class="span1" style="position:relative;top:10px">
<div class="span10">
<div class="row">
<div class="span2 offset5" style="text-align:right">
<div class="navbar-text">
<p><a href="#">Login</a></p>
</div>
</div>
<div class="span2 offset1">
<div class="pull-right">
<form class="navbar-form">
<div class="input-append">
<input class="span2" id="appendedInputButtons" type="text">
<button class="btn" type="button">Search</button>
</div>
</form>
</div>
</div>
</div>
<div class="row">
<div class="span10">
<ul class="nav pull-right">
<li><a href="#">Page 1</a></li>
<li class="divider-vertical"></li>
<li><a href="#">Page 2</a></li>
<li class="divider-vertical"></li>
<li><a href="#">Page 3</a></li>
<li class="divider-vertical"></li>
<li><a href="#">Page 4</a></li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
TWITTER BOOTSTRAP 3 UPDATES:
The markup for TBS3's navbar changed slighty, as did their scaffolding. Here are two replications of the my original solution, one that matches the original exactly and a variation.
Exact Replication
http://jsfiddle.net/technotarek/t67Ms/
Replication with Full Width Navbar
http://jsfiddle.net/technotarek/HxvLS/
(Hint, you can adjust the second replication so that all of the internal elements span the entire navbar by removing the div.container element that follows immediately after the nav tag.)
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