I made a similar suggestion a while back on uservoice, but it was declined at the time.  I'll reproduce it here since it is similar (but not exactly the same) as your suggestion.

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**<a href="http://stackoverflow.uservoice.com/pages/1722-general/suggestions/102248-tag-suggestions-tooltip-steals-focus-when-dismissed">Tag suggestions tooltip steals focus when dismissed</a>**

> 1. Start creating a new question.
> 2. In the "Tags" box, type "java".  
> => The suggestions tooltip appears, showing "java", "javascript", etc.
> 3. Click in the main edit area (where you would actually type the question).
> 
> Expected: Focus goes to the question area so I can type my question.
> 
> Actual: Focus goes to the question area very briefly, then the the tag suggestions tooltip disappears, and when it disappears it gives focus to the tags edit box.