Stat is a software application that can be installed on top of an Operating System, so if your Cloud provide supports the major Operating Systems (Windows, Linux...), then Stat can be installed on top of these operating systems.
Basically Stat works the same way as being in a virtualized environment, but usually being on Cloud you will naturally need more network support since you will need to open firewall ports or translate IP Addresses. In this case, this is completely outside of Stat and your network team or
the Cloud provider network team should be involved.
A Special Note for Stat 6.3 which will support PeopleTools 8.57 that is released only on Cloud.
You can take a look at the Stat Release Notes to know the Stat specific requirements.