Yes, you can upload the EXE to your server and have your customers download it.
It’s possible to generate activation keys from a server, but you need to have a way to ask user for their system ID if you create hardware-locked activation keys.
We provide a key generator in PHP for registered users.
This system ID is mandatory for generating hardware-locked activation keys. This could be a form hosted on your server for instance.
Of course, users can’t generate their own trial key themselves, because they need the Application Master key to generate keys for your application. Unless you publish it, they can’t guess it, so they can’t create keys for your applications.