If by that you mean the search field in a google page, yes you can, for example with a greasemonkey script.
However, I see little point in that -- searching from the location bar just seems easier to me. CTRL-t gets you a new tab with focus in the location bar from anywhere, and I don't have to wait for any page to load to type in the query. Even if google is fast, it's still not as fast.
Also, you can set up other easy searches. For example, stuff I have used in the past 2 hours:
- gis (google image search)
- gfi (google finance)
- listof (google I feel lucky, site:wikipedia.org with search string "list of %s")
However, I see little point in that -- searching from the location bar just seems easier to me. CTRL-t gets you a new tab with focus in the location bar from anywhere, and I don't have to wait for any page to load to type in the query. Even if google is fast, it's still not as fast.
Also, you can set up other easy searches. For example, stuff I have used in the past 2 hours:
- gis (google image search)
- gfi (google finance)
- listof (google I feel lucky, site:wikipedia.org with search string "list of %s")