I think that the the most important information is missing: what is the underlying bookkeeping system.
While reporting on the cash basis is for me, as accountant, OK, I can not accept cash basis bookkeeping. Simply because, if taken literally as defined, it is not comprehensive - it does not provide for recording of indispensable managerial information, such as liability for electricity bill, because it does not recognize transaction without cash flow. So, where would I keep the information on how much and when I have to pay something. In the case of receivable, where the transaction can initially be recognized because there is a cash flow, the problem is, for example, what to do with noncollectable receivable. And there must be some records on assets used by certain entity.
Consequently, there must be a system containing information about stocks and flows which are presented in GFS reports. For me, the double entry bookkeeping system is today a natural choice, but it can be also a single entry system. The problem could be consolidation of the data for the higher levels, for which GFS report are compiled, but the essence is that the needed data exist somewhere.
As a conclusion, there should be no obstacle to prepare GFS 2001 reports, even if budget execution reports or general purpose financial statements are prepared on the cash basis. The quality of the data is, of course important, but in the sense of the question, another story.