I think your are right, SAPUI5 Applications are stateless. I also think that the real point is if the REST services used by teh SAPUI5 Apps are statefull or stateless. It's when SAPUI5 consumes an OData,/JSON/XML service that the state on the backend can be relevant. There you can keep locks and leverage ABAP internal tables across requests.
If I got the question, you should evaluate the type of REST service and the technology behind it.
I always try to avoid statefull REST services but if really have a good reason, I can confirm that you can using a BSP App or a SICF Handler or take advantage of the great Neptune Application Designer that indeed provides a flag at application level for stateless (default) or statefull. Check out http://scn.sap.com/community/mobile/blog/2013/07/22/getting-started-with-neptune-and-sapui5-mobile