No, he doesn't touch the jewels.

Nervous about the power, he decides not to worry about it. Instead of focusing on the translation of the Shepherd's Journal. He continued with the expedition with the rest of the crew who he meets on the way. However, he did tried to keep an eye on the Journal which contained all of the information of Atlantis, as well as the six strange stones.

However, he didn't keep an eye on it well enough...

Because he had to sleep some time which left the Journal unguarded for a period of time. Enough for one or more people to be able to handle the book. Now normally people wouldn't be too interested in a book they can't read. However, given the fact Commander Rourke had found a great power source in the book which could make them millions, it becomes more tempting as they looked for more sources of riches.

Which is why people would be stalking around where Milo was sleeping with the Journal. Why they could come into contact with one or more of the Infinity Gems.