Yes, they did.
To begin with, as Ragnar Danneskjöld told Hank Reardon,
Do you know the condition of existence in those People's States? Since production and trade - not violence - were decreed to be crimes, the best men of Europe had no choice but to become criminals. The slave-drivers of those States are kept in power by the handouts from their fellow looters in countries not yet fully drained, such as this country.
Right after finding out the exact nature of Project X, Robert Stadler objected to the (supposed) necessity of it, pointing out that
With the whole world starving and all of those People's States barely subsisting on handouts from this country - where do you see any danger of war?
Later, Hank Reardon said
Have you anything left to loot? If you didn't see the nature of your policy before - it's not possible that you don't see it now. Look around you. All those damned People's States all over the earth have been existing only on the handouts which you squeezed for them out of this country. But you - you have no place left to sponge on or mooch from. No country on the face of the globe. This was the greatest and last. You've drained it. You've milked it dry. Of all that irretrievable splendor, I'm only one remnant, the last. What will you do, you and your People's Globe, after you've finished me? What are you hoping for? What do you see ahead - except plain, stark, animal starvation?
That being said, once production was shut down in the U.S., there'd be nothing left to "prop up" the socialist governments. Presumably, they'd collapse.
Secondly, John Galt's speech evidently was carried everywhere in the world. Originally, Mr. Thompson was supposed to broadcast a speech that would be broadcast globally on every radio station and television channel.
...the front pages of the newspapers and the shouts of the radio voices had explained it: "To counteract the fears and rumors spread by the enemies of the people, Mr. Thompson will address the country on November 22... Mr. Thompson's address will be carried by every radio station in this country and in all countries throughout the world, wherever radio waves may still be heard."
Given that John Galt gave a speech instead of Mr. Thompson, presumably his speech was heard everywhere that Mr. Thompson's speech would've been heard. While John Galt chose not to broadcast on television, his speech would have presumably been heard globally via radio.