According to a report in All About Samsung, the region-locks are only valid for the first-time activation of the smartphone. So, you are planning to get an American Galaxy Note 3, you will have to activate it using a SIM card valid in Americas region and after the activation, you can pop in any SIM card to use it. The same has been tried and tested and works fine.
Apparently, Samsung wants to curb the grey market imports of smartphones from one region to another. So, unless you open the smartphone box and put a local SIM to activate it, there is no way to use it in another region (except a few exceptions).
These exceptions are that a local Samsung service center (local to the place from where you have bought the phone) can unlock the phone for you or you can try one of the services available online, which offer unlock codes for money.
In related news, it has also come to light that region locks aren’t just present on Note 3, units of Samsung Galaxy S III, Galaxy S II, Galaxy Note, Galaxy S4 and Galaxy S4 Mini, which were manufactured after July 2013, come with region locks. All these region locks are also valid for the first time activation like Note 3.
It is also important to note here that not every region seem to have region-locked Samsung phones and unless you see a sticker like the one present in the image, it is very likely that the phone is not region-locked.