Is there any significance (or link to the white rock in Sinnoh, that activates the Shaymin in-game event) to the white rock by Mossdeep's Space Center in Pokémon Ruby/Sapphire/Emerald?

No, there's no significance. Some people have said if you do something then you can go outside and do something with the rock, which is part of an alleged, but untrue, in-game Deoxys event. The white rock in Hoenn is just sorta.... there.

No. I'm sorry to say there is real purpose for the rock there. But there are several rumours involving it and the space centre.

In the games, a man by the window will reveal the number of successful launches there have been; the number is an indicator to the number of weeks since the saved game was begun. Because this is a time-based event, the Space Center will cease to launch Rockets when the battery for the internal clock runs dry.

Many rumors have been spread about this number and its relation to Jirachi and Deoxys. Many believe that if the man reaches a certain number, the player will be able to ride a rocket into space and battle Jirachi or Deoxys. Like the truck rumors of Generation I, this rumor is false.

Also, there is a rumor that involves the Shaymin event at Route 224. It's that when Professor Oak said that there was another white rock in Kanto, it could have been a mistake, and that the programmers meant the white rock near here. This has yet to be proven, since no remakes to Ruby and Sapphire have been made.

(Credit to Bulbapedia for those.)

Don't listen to the Wish Tag rumor and the Deoxys rumor, they have been proven to be hoaxes.

Not that I know of...but if there is a remake of the games (Ruby,Sapphire and Emerald) maybe there will be but also there is an error as it says the white rock was in Kanto but there is probably no relation in the two rocks

oh hell yes did you NOT know that Shaymin is from space!? *sarcastic*
no i dont think they're is, besides what has a gratitude pokemon that is 'grass' type got to do with space anyway?

There is no one knows but the game creators through