The way your question is phrased, the only possible answer is to test, just as Izquierdo says. I'd use other types of tests like usability tests and probably measure with Hick-Hyman's Law, but the bottom line is you'll need to test it.
If your question refers to the need for clues to search actions (whether they are symbols or not), then the answer is yes.
Perform an A/B test.
An ideal way would be to add icons to an existing production site and measure the time it takes them vs. a group that doesn't see icons. If it's not possible to do a test on the actual site, you could recruit users and use a sandbox site or prototypes.
If the icons help users find their results more quickly, you could take that ...
I think the easiest and most plain answer is:
If your website is all about searching (like google), you should autofocus the search field.
If you website is not mainly about searching, you shouldn't autofocus the search field.
The main goal of a design is, to provide information as clear and easy as possible to the users. You do not want your ...
Tl,dr; some reasons not to give the search field autofocus when entering a site are:
Searching is not the main function of your site, just an optional tool you offer to your users
Searching is the main function of your site, but it requires more than 1 field/parameter to work
Google does this not because 99.9% of its users will search; it does it because ...
Here is an example of where auto focusing the search field is extremely annoying, unwanted behaviour:
Go to Openclipart and search for something, say linux.
Scroll down to the bottom and click the next page button.
Now on the second page result you want to scroll down the page by pressing the spacebar.
Except you can't because the stupid search box has ...
Autofocus is a tool that is wildly helpful if done correctly and it is appropriate to the situation, but there are many, many things that can go wrong. If your implementation doesn't avoid all of these pitfalls then you will cause great annoyance to some (or maybe all) of your users:
If the autofocus happens only when the page has finished loading, then ...
You already answered your own question. Keyboard/screen-reader users will need to step out of the search field when it was focused automatically to make use of other ways to navigate. Also on mobile, Google doesn't auto focus on the input field. The reason is simply to not directly popup a keyboard since that would be annoying.
If you want to make your main ...