Most of the time NO !!
Depends on application to application. Only mutlithreaded software that can use 2 or more cores will benefit from a quad core, for e.g., video encoding. But u will feel that the system is more responsive when juggling multiple loads:)
But first of all, i highly doubt u'll be able to upgrade ur laptops CPU so easily....have u checked if the quad has the same socket and TDP envelop?? It would be really helpful if u could mention the complete details of ur current and planned future processor