Yes,it's possible, this is especially useful during development or setup phase.

There are 2 way to access the mobile website in the desktop browser. If the site is not on live production you can enable the 'Switch always' option (see image below), this will have the effect to make the mobile version of the site available for all browsers and devices.

Otherwise you can switch to mobile template appending the string ?template=responsivizer to urls, for example www.mysite.com/?template=responsivizer

If the second solution of appending the string ?template=responsivizer is not working on your site, ensure that this feature is available in your Joomla installation and it's not blocked by some secutiry extension such as Akeeba Admin Tools.