But the devil is always in the detail...

TBH I'm not very familiar with the Processmaker appliance, but all TurnKey v13.x appliances are Debian Wheezy (aka 7) so as long as the software will run on Wheezy then it should be installable. Note that you may (or may not) need to increase the size of your server (depending on system requirements of the additional software).

Personally they way I would approach this is to download the Processmaker appliance and run it within a local VM. Then have a read of the install instructions (that relate to Linux/Debian) and have a go. IMO it is iperative to take careful notes along the way. That way if something messes up, you can just wipe it and start from scratch. Also you can then easily reinstal the software on your 'real' (i.e. cloud) server. Also make sure that you run a backup of your server and test it before you go fiddling with your production server!