Can background image extend beyond div\'s borders? Does overflow: visible apply to this?
not possible to set a background image 'outside' it's element,
BUT YOU CAN DO what you want with using 'PSEUDO' element and make that whatever size you want and position it wherever you want.
see here :
i have set the arrow outside the span

here is the code
HTML :
dasdasda
strong text
.tooltip{position:relative; float:left;}
.tooltip .msg {font-size:12px;
background-color:#fff9ea;
border:2px #e1ca82 solid;
border-radius:5px;
background-position:left;
position:absolute;
padding:4px 5px 4px 10px;
top:0%; left:104%;
z-index:9000; position:absolute; max-width:250px;clear:both;
min-width:150px;}
.tooltip .msg:before {
background:url(tool_tip.png);
background-repeat:no-repeat;
content: " ";
display: block;
height: 20px;
position: absolute;
left:-10px; top:1px;
width: 20px;
z-index: -1;
}
see here example: http://jsfiddle.net/568Zy/11/