It depends on the situation, but generally, the answer is even if you could it possibly won't be worth while.
You can though, (at least on a desktop PC), type when most combo box is expaneded/selected to find a value... If you visit the DHL site you will see a drop down list. Click the list to see the options and whilst it's open type
United K (including the space) and you'll see it will jump to the item.
Things like Greasemonkey will allow you to affect the rendered HTML and possibly convert it from a combox box to a search box, but, the thing about a combo box is it's predictable! We know what options we have and therefore, what can be selected. We don't typically code against unexpected value errors since there isn't likely to be any! This may mean by typing in words which don't exist could result in unexpected behaviour.
With web apps, it's potentially more complicated as other technologies can be used...
And of course, each browser may react differently too, so in conclusion it's not really possible to answer, but my answer is no, you can't do what you want without error (or at least, working exactly how you want) for every webpage!