Members Search: Auto select the search box

There are numerous occasions where it is necessary to add members to courses or sections. On each of these pages, it is often necessary to search for individual names as the list of names (unless you know what group they are in) is very long.

I find myself doing one of two things when adding members (ex: adding an instructor or adding students):
1) Selecting the group the member is in from the drop down list.
2) Searching part of the memberś name to filter the list.

Since the search box is such an important part of this process of filtering. I am wondering if it is possible to have the box selected and ready for input when the page loads so that a person can just start typing the members name rather than having to click in the box and then start typing. It would make things much simpler and would allow for much faster input of names if the box was ready for text input (hilighting the text already inside) after every action on these pages. This would mean that typing names and then pressing the enter key (to filter the list - possibly pressing enter again if there is only one member after being filtered) then typing the new name and pressing enter... would be the process.

In general I think that having the search box selected and ready for input at all times would make things much easier. Is this possible?