The short answer is: No.
The long answer is: Yes, if the app was written in Qt 5 or HTML, and was capable of running on the limit screen size and interacting with touch input and on-screen-keyboard, then it would run. But most apps written originally for the desktop won't meet that criteria.
The even longer answer is: This is why we developed the Ubuntu SDK, it's a toolkit designed to allow apps to be developed for desktops, phones and tablets (and TVs). It has resolution-independence built it, it support multiple display servers already, and it's being designed to adapt appropriately between touch and keyboard/mouse inputs. Eventually we hope that the majority of Ubuntu's apps will work seemlessly across all of our supported form factors, and the Ubuntu SDK is how we plan to get there.