As long as they still have access to local persistent disk (and nearly all Azure offerings do in one way or another) they'll be fine. Just don't park the VistaDB database file on a temp disk.
I think they are planning to move to MS Azure. This one system I use a lot of DDA. Changing all to SQL will be a lot of work. Right now its stored in a in house server and I have to let the client know what it will take to move to cloud
Broadly speaking it shouldn't change anything about using VistaDB, but to be completely sure can you clarify what you mean by a cloud server?