Does google crawl the mobile version of a website? I would think not, since the user agent would be that of the google bot.
If it doesn't crawl it, does it mean that having a mobile version of a website has little impact on the page rank?
Well, the answer to your question is twofold:
A mobile version of your website will not have an impact on your desktop version, since the sites are targeted at different user groups.
Google does have a dedicated mobile bot, the Googlebot-Mobile. So this bot will crawl, index and rank your mobile version. Important fact to know, if you want your mobile website to be ranked within the search results of Google's mobile search on mobile devices. The mobile version of your site will be preferred to the desktop one on mobile devices.