32 bit Unity project > 64 bit WebGL build?

Here's a question:
I am using Unity 32bit to create projects. Originally I used Webplayer to build the projects for the browser but obviously, this has ceased to be an option in the Unity 5.
Now, My son has a 64bit super-dooper PC. Is it possible to install Unity 5 64bit on his PC and for me to save my project on my external hard drive, plug it into his PC and fire up his 64bit Unity to save/build the project for WebGL?
So, in a nutshell, I make a game in my 32 bit Unity and build it in his 64bit Unity?

thanks for the advice.
R