Yes, a range hood can vent out the wall that it is against. I am not sure what you mean by "and then up" in this context. The blower on my hood has the vent pointing upwards. I put an elbow on that hole and directed it straight out the wall. I am under the understanding that some vent blowers have a hole on the rear, facing sideways, but I do not know this for a fact.

Ours vents directly outside - it is only a 350 CFM and is pretty quiet - a remote fan is the quietest - also not sure what you meant by out and then up.

Do you mean connected to a vertical pipe that goes up the outside, to (for instance) distance the vent from an outdoor living area? I think in theory that would work, as it works on the inside, except for the problem of condensation inside the pipe. Maybe someone with more experience can suggest a solution to that problem, possibly an enclosed, insulated chase?