The noun dearth, meaning a scarce supply, is synonymous with shortage and scarcity. A time of dearth is one in which things are dear—dear being the root of dearth—so there are things, just not many or much of them. So, at least traditionally, dearth does not mean a complete lack or absence. For example, if you have $12.43 in your bank account, you have a dearth of funds. If you have $0.00 in your account, you don’t even have enough for a dearth. So phrases like complete dearth and total dearth are as logical as total shortage and complete scarcity.
These writers use dearth in the traditional sense:
Aleksandar Hemon points to this dearth of translated literature in his introduction to Best European Fiction 2010, a new anthology. [NHPR]
And these cases, dearth means complete lack or absence, which is a little different from its traditional meaning:
Rare books cataloging systems and the utter dearth of work on pre-nineteenth century paintings makes locating earlier work a difficult task. [Appositions]
That is, Trekkies who are willing to overlook brain-lockingly repetitive gameplay, unvaried design, thin storytelling, buggy client software and an almost complete dearth of meaningful social interaction. [NY Times]