I have spent so many hours researching this and I still can't figure out what the right answer is.
Can the Verizon Galaxy S3 (unlocked) be used on an overseas GSM network by inserting a local SIM card? Its supposed to be an "international" phone, and I read various forum posts where people say the S3 has a GSM radio,and that a recent firmware update enabled the GSM radio. But, I don't see anything about GSM in the S3 specs.

Spec from Verizon web site:
Network: LTE, CDMA/PCS/1xEVDO Rev. A (800/1900 MHz)

I *just* went to a Verizon store to ask this question, and I was told that you can only use the phone internationally on CDMA networks, not GSM. Seems to me that if it is CDMA only then that greatly reduces the usefulness of the phone. And yes I know, people that work at the phone stores don't always give you the correct answers...

So has anybody actually used a GSM SIM card overseas and did it work?

 

The guy at the Verizon store said Verizon will not unlock the phone until 6 months after purchase (for new customers). I can't wait that long.
So next question: If I root and flash the phone with a custom ROM, will the phone then be unlocked?

 

Update on my problem. Today I called Verizon and asked about using my phone overseas. The international tech support person told me the exact opposite of what I was told at the Verizon store. He said that the Galaxy S3 *does* work on GSM networks overseas, if I insert a SIM card, and he said that the phone is unlocked as of right now as long as I have the latest firmware installed.

 

Next update to my problem: I went to Mexico and bought a GSM SIM card (IUSACell). I put it in and could not connect to the network. IUSACell is a Mexico telecom and they use 850/1900 GSM. That made me think that the phone was not unlocked or was not GSM compatible.

Then I came back to the USA and tried the Mexico SIM again and this time it connects (roaming). In settings I can force it to search for GSM providers and I can see both AT&T and T-Mobile! So that tells me it does have GSM capability. But when I try to manually select AT&T or T-Mobile, both times it says "Cannot connect to Network". But when I select Global Mode, it does connect to a network but I can't figure out what network it is connecting to. Maybe it is connecting through Verizon, I don't know.
So now I am even more confused and I still don't know how to get my phone to work overseas.

 

Ok, more researching leads me to believe that Verizon totally blocks using AT&T or T-Mobile networks for roaming or any other use. So when I insert my Mexico SIM card in the phone while I'm in the USA, I guess it is roaming on Verizon.

The amount of time I am wasting trying to figure out this phone is not worth it. I am very close to just buying a new phone for international use.

 

Did not connect at all. No signal bars. Could not make a call or SMS.
(BTW I am already aware of the issue that the GS3 can't be used for data because of an APN issue/bug).

 

That is very odd because the specs from Verizon's website doesn't list either of those frequencies.

Spec from Verizon web site:
Network: LTE, CDMA/PCS/1xEVDO Rev. A (800/1900 MHz)

 

Global: GPRS/EDGE/GSM (850/900/1800/1900); HSPA/UMTS (2100)

Aha! Now I see it. My browser was only showing me the mobile version of VZN's web site. I changed browsers and now I see the full site with the full specs.

Now it is an even bigger mystery. Why didn't my phone work on the Mexico GSM network...

 

I finally got my phone to work with a foreign SIM card. I bought a Mexico IUSACell SIM card a couple weeks ago and I never could get it to work on multiple trips to Mexico.
So I bought a SIM card form a different carrier called Movistar and it works perfectly. I even have a data connection at ~150kbps. I also tried a friends Telcel SIM and that one works also.
So my mystery is solved: Verizon Galaxy S3 with the latest firmware update is GSM enabled and unlocked for use overseas. But apparently, it works with some GSM providers but not others.

 

I would love to know why an IUSACell SIM does not work on the stock ROM but it will probably be a mystery forever. I could call Verizon and ask them. Hahaha just kidding, what a waste of time that would be...