Yes, it is possible to read iOS class variables from outside of an app. Depending on your perspective and proclivity towards jailed or jailbroken devices, you may find a few ways to read them at runtime or in-memory.
Via runtime, on a jailbroken device, a tool such as NCC Group Introspy is a developer-friendly tool that doesn't require any formal reverse engineering exposure or experience.
For accessing memory in the iOS Simulator or on an iOS device, lldb and gdb can be utilized to dump an app's current memory state. One would need to identify the process to be dumped and perhaps overcome any self-modifying or self-checking code that would include process dumping. This typically requires either a Unix or a reverse engineering background. As a lighter approach, Xcode does provide a debugger, notification spy, and a DTrace interface. One common way of accessing memory without a debugger is to get an app to crash and then go through the artifacts found via the Xcode Organizer. Another way in the iOS Simulator is to go into the menu option Hardware and select the Simulate Memory Warning option.
For those who do have reverse engineering experience and a jailbroken device, be sure to check out Snoop-IT as a first-rate tool to go deeper than what Introspy above provides. Snoop-IT is also heavily covered in the books The Mobile Application Hacker's Handbook as well as Learning iOS Penetration Testing. However, my top recommendation for those who have gdb experience is to follow the techniques outlined by NetSPI to get access to the full app heap. Other techniques include using lldb on a jailbroken device by using a debugserver, which is even more-detailed on the mSecLab blog, but also covered on versprite, isa56k, and a bit on lldbpy via lifeform-labs. The last technique I might mention for jailbroken devices (or for any OS X install) is the kdv tool which utilizes the KDebug mechanism, although certainly other kernel memory dumping options are available such as readkmem. MEMSCAN and Radare (see the NetSPI blog post about adding the Radare repo to Cydia) can also be used to search through or dump process memory on an iOS jailbroken device.
There are a few techniques that can be accomplished while in the iOS Simulator. The recent book iOS Application Security covers many of these in-depth. I might also recommend that you check out some anti-anti-reversing techniques such as the ones typically done on OS X, as they will also apply to iOS. For example, a game trainer for OS X called Bit Slicer and its underlying techniques can be mapped. Basic problems with debugging (e.g., if the NetSPI gdb technique above does not work) can be worked out with idapython as seen when this author ran into a problem with anti-debugging during a MyWi reversing effort. As this article on anti-anti-debugging suggests, a catalog of techniques formalized as a GitHub project called pangu can be bypassed by another GitHub project named Onyx-the-Black-Cat. There are many other reversing challenges, so I suggest you check out the ReverseEngineering.StackExchange tagset for iOS or similar resource.
For jailed devices, I suggest you look into repackaging apps with cycript and/or Frida. If you can get a remote cycript shell, then you can use the mSecLab methods for analyzing memory of an app as one would do on a jailbroken device.