Your draggable DIV can be wrapped into another div that won't allow scrollbars to be created.
<style>
.wrapper {
height: 100%;
position: absolute;
width: 100%;
overflow: hidden;
top: 0;
left: 0;
}
.draggable {
position: absolute;
top: 1000px; /* simulating going over the edge of the page */
left: 800px; /* simulating going over the edge of the page */
width: 500px;
height: 500px;
background: #F00;
}
</style>
<div class="wrapper">
<div class="draggable">
Hello - No scrollbars created for me. :)
</div>
</div>