The short answer to this is "yes, yes and thrice yes"!
What is Google Webmaster Tools?
Google holds a lot of information about nearly every website on the Internet (it is impossible to hold information about every website as new websites are appearing every second). Which means that they probably hold a lot of information about your website.
Google Webmaster Tools allows you to see some of this information. The information they let you see is extensive and invaluable.
For example, you can register your XML site map with Google and you will be able to see reports as to how well it is working for you. Registering a site map with Google is the quickest way to get your new website indexed by Google.
It also gives useful information about search queries used to find your website, useful for researching for the purposes of Search Engine Optimisation.
However, if there is only one reason to use Google Webmaster Tools it is this:
It Lists Errors That Google Has Found on Your Website
There is a section where errors or problems have been found with your website generally or on specific pages. Things like titles that are too long or too short, problems accessing your pages and slow download times.
It is like having a free monitoring service for your website so you can fix problems as soon as they arise instead of waiting for them to harm your position in the search engine results pages.
How Much Should it Cost to Implement Google Webmaster Tools on my Website?
Signing up with Google is simple and it is free. Nor should your web designer charge you for it to be added as it is no more difficult than uploading a simple identification file that Google provides.
So why hesitate? Add it to your website today. it will cost you nothing and is essential to your business. You won't regret it.