Okay, numerous hours later I've almost got a solution to this.

Edit: Now have got a solution, make sure you read the updates at the bottom of answer.

Probably will prove very useful to any stores that require SKU codes to be searchable or have a number of products that contain special characters because now at last, by implementing the below, Magento's search will return results for these search queries.

After some debugging, I identified that the URL's were being encoded (twice) in Url.php located at /app/code/core/Mage/Core/Model.

$query = http_build_query($params, '', $escape ? '&' : '&');

As pointed out in function getSearchUrl in /app/code/core/Mage/CatalogSearch/Block/Term.php.

public function getSearchUrl($obj)
{
    $url = Mage::getModel('core/url');
    /*
    * url encoding will be done in Url.php http_build_query
    * so no need to explicitly called urlencode for the text
    */
    $url->setQueryParam('q', $obj->getName());
    return $url->getUrl('catalogsearch/result');
}

So at this point, I knew I needed to reverse urlencode and output this result instead of the escaped query for search.

I was able to reverse this process using the following:-

$noescape = preg_replace("/%u([0-9a-f]{3,4})/i","&#x\\1;",urldecode($this->_queryText));

Adding this to function getQueryText in /app/code/core/Mage/CatalogSearch/Helper/Data.php then allowed me to return the non escaped query text with $noescape so I simply add a new function in Data.php underneath getEscapedQueryText like so:-

/**
 * Retrieve search query without escaping special characters
 *
 * @return string
 */
public function getNoEscapedQueryText()
{
    return $noescape;
}

Now all I need to do is figure what code is outputting the query in the URL so I can modify this to use $noescape but struggling to find this at present. Will update my answer as soon as I find it.

Update

I know that return $this->_queryText; is what is outputting the search query in the URL now, I just haven't figured out how to incorporate the above into this output (I haven't managed to figure out the correct syntax).

Currently fiddling about with variations of

return $this->preg_replace("/%u([0-9a-f]{3,4})/i","&#x\\1;",urldecode($this->_queryText));

and

return $noescape($this->_queryText);

Update 2

$noescape above can now be ignored as we can just modify return $this->_queryText; directly with:-

return $this->_queryText = preg_replace("/%u([0-9a-f]{3,4})/i","&#x\\1;",urldecode($this->_queryText));

End result is that we can now use special characters in Magento's search field that returns results and doesn't escape them to %252F2 for example. The URL's will still contain the likes of %252F2 but it retains the special characters in the search field via getQueryText so it still resolves the problem.