Not necessarily. A simpler option can just be to create a new user account, add it to the local administrators group then login with that account and install use the software. In some rare circumstances this has resolved login/connectivity issues where the original profile was corrupted somehow.
VM's can also work, but not all users are tech savvy enough to install/maintain this type of setup inclusive of additional licences where 3 month trial versions need activation etc.
As a general rule of thumb, if the PC is a users PC ( not corporate/School owned ) then it's unlikely that local firewall will be the issue as default rules are to allow outgoing traffic by default. However School machines will most likely have policies/whitelists in place for Security policy of the school admins where changes could be requested.
If using VM, then install the OS, software get it working then snapshot it, you can always revert back to this state if there is an issue. Usually built in functionality at least in Open-Box and VMWare workstation.
But as above, a clean new local account maybe a better way forward depending on why communication is blocked.
Set an allow rule for *.e-marker.co.uk. port 80 & 443 should be all that is required though this would be more likely needed on the ISP/School Network policy rather than a personal Pc.