Hello RZN, and welcome to Seven Forums.
It would not be a good idea to have the page file on an external drive. If it was disconnected by mistake, you would lose all data in the page file and could cause issues with any program or action that may have been using the page file at that moment.
It would be best to keep the page file on the fastest internal HDD or SSD for better performance, and set to be managed by Windows 7.
Hope this helps,