Can I access an account that was created as a "Network Account"?
You can use Back to My Mac and access it there. There is a support question on Apple's website that explains how to set it up on both Macs. I should tell you that the requirements are as follows:


Your Macs need to be running at least 10.7 or higher (you said your iMac is running 10.8.5, so your iMac should be good; don't know about your other computer though),
an iCloud account,
and both Macs need to be connected to a router that supports router that supports either Universal Plug and Play (UPnP) or NAT Port Mapping Protocol (NAT-PMP) with either of those features enabled (you can check your manual of the routers to know how, but most modern routers should have either one or both turned on).


I forgot to mention that you should also check off the "Screen Sharing" and "File Sharing" boxes from System Preferences > Sharing.

Be sure that when you have enabled Back to My Mac in the iCloud settings in System Preferences, it should not have a yellow warning sign. If it does, click on it and follow the instructions there.

When both Macs have been set up, go to the Mac that you want to use to access the other and go to Finder. You should see the name of the computer there. Click on it.

You should see a bar with two icons: "Share Screen…" and "Connect As…". Click on "Connect As…". You should now see a box with a username field and password field. Type in the account that you wish to access and click "Connect." You should be able to access the files from there.