Are there any known limitations in developing an application in Appian without a

No "problems" per se, but NOT using an RDBMS in conjunction with Appian removes a very useful tool from your toolbox. You are limiting yourself to just using process data and making your app less flexible.
There is no need at this point, but what if there is one in the future? Are you going to migrate data out of Appian then? What if other applications, in Appian or external would like to use that data?
Every good Appian application design NEEDS to persist data in RDBMS.

Thanks Mike. Concur with your observation - however a design pattern which will move process data to an external data store via a webservice - could be based on an event(eg Process completion) will also suffice right? It will cater to future reporting capabilities as well. Thoughts?