The answer to that question... Is in fact yes.
The technology behind the web hosting companies can affect how well your website ranks within the search engines.
This is mainly to do with where your website hosting provider has its servers located; and whether the website which you are trying to rank for within that local area is hosted within that country.
IE. A website that you would like to rank well in the UK for a keyword should be hosted within the UK in order to get the best results. For example, Giraffe Digital; a High Performance Web Hosting host their website locally for better search engine rankings. Another example of good search engine optimisation (SEO) is a Highway Contrator company such as Traffic Management Solutions Kent whose website ranks well for their chosen keywords because of the relevant content related to their Traffic Management Company.
Another loca firm that uses the servers of Giraffe Hosting is Complete Brickwork Solutions, a brickwork specialist firm based in Maidstone, Kent. They use Giraffe Hosting because their services are fast loading and provide 1st class support to their clients.