If the page is indexed on Google, you'd be able to plus one it from the search results page. You must be logged into your account to do so. To see if the page may be indexed, you can use - site:yourdomain.com "keyword"
In addition to what 5starpix said - you can only plus one from the search results if the plus one symbol is shown next to the listing.
If there is no G+ button 2nd way to Plus your site is while you are searching the content in google, then also appears the +1 button you can plus that site during searching. Another way to plus your site is just login with your plus account and share the URL of the site there.
maybe i don't understand you well, but you can just copy url and post it g+... is this not a good idea?
...I made the mistake of recently searching on google without having anything to block javascript and...wow...is this what the internet looks like to most people? Then I tried using IE and wanted to cry because I know this is how people see the Internet. /painfulrant. That being said...doesn't google allow to +1 any site? It has nothing to do with submitting the site or having it be part of Google+, isn't the idea that you can + anything you like and people who have Google+ will see the sites that are +'ed the most and that will be part of their new personalized search algorithm/privacy policy due to be set on March 1st?
copy the url and post it into the google search box. if its indexed you will be able to +1 it on the SERPs
to check te no of goole plus for any link you can use the following code in address bar plusone.google.com/u/0/_/+1/fastbutton?url=http://www.googleplus1fast.com/