Is it possible to make light travel through world portals?

No, since VRAD has no knowledge of them when computing lighting. What you can do (if space behind the portal permits) is build a small replica of the other side out of nodraw, and add copies of the lights there. That way the light mixes with the other side nicely. You might also want to add a border or frame around the portal using models, to disguise the lighting change. Doors work pretty well for this.

Okay, thanks. Your advice about the border item really helped. I also used the same light colors from the other room, but at a lower brightness.