Yes, but it would require some major surgery, a bit beyond the scope of this forum. You might wish to hire some assistance at http://jobs.wordpress.net/.
Another option would be to keep the widget the way it is on mobile and only switch to the floating version on larger screens using media queries:
@media screen and (min-width: 600px) {
#text-15 {
position: fixed;
top: 25%;
right: 0;
z-index: 20;
}
}
This code tells the browser that when the window is 600 pixels wide or larger, set the text widget to a fixed position, floating above the rest of the site. When the browser is 599 pixels wide or smaller, the widget will stay where it was before.