No, this is a premium offering from Mendix, so the free license won’t be suitable. 

https://docs.mendix.com/developerportal/deploy/private-cloud/#licensing

I hope this helps.

If you use private cloud on aws, google, etc, you can use their existing load balancer, so you can have a public url by connecting your mendix ingress to provider LB. If you are using openshift on local, you can use openshift route and get url that can be accessed locally. If you are using kubernetes, you can use ingress controller (e.g. nginx ingress controller) and metallb (simulates load balancer controller like in the cloud), then you can add to dns or local /etc/hosts with appurl bind to ingress’s service ip.