|Short answer, No. Long answer, maybe - but probably not.|
It all depends on what this program is and how it works. Some programs are built to work within such an environment, but if that was the case ou would probably know it. If not, there are sometimes ways to build a server-side solution to hook into the application. For example, lets say the program allows you to convert an image into a PDF. You could build a web solution that allows the user to upload a file, then runs the exe on the servver and then allows the usr to view/download the output.
But, if this is a program that has it's own interface that the user needs to interact with then the answer is NO - with an exception.
There is software that allows you to "port" software via the web (e.g. Citrix), but it is typically expensive and not something for a novice user to implement.