Any standard script will be able to function even in a shared hosting. It may not look like it but surely it will.
Now correctly pointed out as earlier, will your site be able to run on it or not that is a different question all together. What are the specs of the machine you are running on now? Compare them. That might give you some of the idea.
Now correctly pointed out as earlier, will your site be able to run on it or not that is a different question all together. What are the specs of the machine you are running on now? Compare them. That might give you some of the idea.