You can update without being charged. As far as Apple can tell, you have a computer that came with ML. The only draw back to using a pirated copy, is that you can't use the recovery partition to reinstall the OS. Let me find my other post.
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From what I read, any one who downloaded it illegally and updated, can update through the AppStore without an problems.
* Can you install Apple's software updates on this version of OS X?
- Yes. Period. To Apple it looks like a legal, pre-installed version of OS X that came with a new computer, and updates will be delivered via the App Store even though you haven't bought it from there. There's nothing they can do to block you - short of one day starting to check your computer's hardware serial number, and there's no way they're going to alienate and piss off their users like that over $20, so don't worry. Updates will continue to work for you forever.
* Are there any limitations at all compared to a legal copy?
- Yes, there is ONE limitation. The Recovery Mode (entered by booting with Command+Option+R) launches a minimal ~600MB version of OS X with some recovery tools like Disk Utility and Terminal (to allow you to fix a broken OS). It also offers the feature to Re-install OS X; however, since the recovery partition is only ~600MB it doesn't contain the full OS installer, and if you try to use its Re-install option it will actually connect to Apple's servers and verify eligibility based on your computer's Serial Number (for pre-installed copies of the OS) or your AppleID (for App-store copies of the OS) before it will proceed with the full ~4GB installer download. This is the one and only limitation, and it means that you cannot use the recovery partition for a re-install unless you've bought the OS. HOWEVER, you can OF COURSE still use a bootable DVD or USB stick, so there's no need to fear. This limitation is a complete non-issue as long as you keep a copy of the full installer on some external media. Besides, it's a lot faster than waiting for an installer to download over the internet, so you're not missing out on anything!