Yes, they should. Soap operas have a long history of far-fetched story lines so it is not as if they could never bring her back, even as a different character. It may even liven things up and get people talking if they bring her back, which would result in a boost in the ratings.
I think script writers can easily come up with a story arc that explains her absence. I like it when a series values continuity and keeps the same actor on. Viewers get attached to the characters they see on television and it can be jarring to see a sudden change. I think viewers will be more accepting of an explanation in the story rather than a sudden change.
No, General Hospital should not replace Kirsten Storms in her absence. Or, rather, there is no need to replace Storms. Though the soap opera can indeed replace the actress, it has no obligation to replace. The principal argument for this is the nature of the soap opera. It is a television genre that rests on an ongoing plot and does not face any pressure to put an end to the story. Thus, characters can disappear and reemerge as the plot sees best. Such flexibility allows for real world problems to be resolved.
General Hospital should not replace Kirsten Storms in her absence. She has been on the show for a while and it would be odd to have another actress play her in the mean time. They can write her out of the show for a while, saying she went to another country for a vacation.