Access IPhone in Finder
Generally without jailbreaking the device, no. Apple makes it quite difficult to access the filesystem of your iOS device - whether attempting to navigate directories on the device directly, or remotely from your computer.
However, there are certain programs recently made available which enable one to do so. For example, iFunBox is an iOS file management application for your desktop that allows you to browse and manipulate the filesystem without jailbreaking the phone.
Additionally, you may find it helpful to use iOS's Spotlight feature to quickly find and access content on your device:

&quot;To access Spotlight, swipe down on your home screen to reveal the search field.&quot;
&quot;Spotlight searches certain text fields in the content of your device for text beginning with your search phrase. It is not case-sensitive, so you can search using uppercase or lowercase letters and get the same results.&quot;