How to Refresh or Reset Windows 8 without the System Reserved partition?
Without the System Reserved partition everything remains the same, both Troubleshoot and its advanced options show the same options as when having it.
Essentially that's because either having that partition or not doesn't change the fact that Windows installation is successful, boot files are copied to the only partition there is instead of being copied to the reserved partition. The benefit of the reserved partition (or one of them, I don't know if there are more) is that it's not directly accessible to users so it's less probable that important files get corrupted or deleted.
In 2010 they explained what the partition was for in a TechNet blog post, and recently in this website; that partition is used to implement BitLocker (which in Windows 8 is available in Pro and Enterprise versions):
The partition has two main functions. First, it stores the Boot Manager code and the Boot Configuration Database. The second thing it does is store the startup files needed by BitLocker Drive Encryption. If you end up using BitLocker to encrypt your entire hard drive, you don’t have to repartition your system to enable it.
In Windows 7 the size reserved for it was 100MiB, in Windows 8 it was increased to 350MiB. I believe the main reason is that now the recovery image (WinRE, a small environment with tools to help diagnose and recover from errors) is stored there too, which is 191MiB. In Windows 7 it was 161MiB and resided in the main partition (system hidden directory named Recovery).
This is the actual process in a virtual machine without recovery partition:
Selecting to refresh the Windows installation works as expected: after selecting the option the computer will reboot and you'll be prompted to login as an user of that machine. Confirming you want to go on will start the process and begin refreshing, installing drivers, etc.
After the process you'll be able to access the machine with your user, personal files will be there and there may be a file in the desktop containing information about programs that were installed before the process and are not there anymore. Also, any folder that may have been in the Program Files directory will be deleted too (e.g. programs installed manually without and actual installation programs); applications from the Store are installed automatically after refreshing though.
A similar process happens when choosing to reset, but you're not prompted to login since there will be no users in the new system. After the reboot you're presented with the choice of "fully cleaning" the whole drive, which I assume a series of data overwrites are performed to accomplish that:
After the process you'll see the license agreement and you'll go through the first steps you had when installing Windows: preferences, setting up user name, ...
Note that both processes require you to insert a recovery media or Windows DVD, I don't know if that happens having the recovery partition but it's most likely it does; resetting for example erases everything so the original image inside the DVD needs to be applied again.
I think it's important to mention too that Windows activation is backed up and restored during any of the processes, whether Internet access is available or not (so people using the Enterprise evaluation won't be able to reset the trial period with this, although a reset isn't very different than a clean installation).