No, despite rumors to the contrary, there is absolutely no clinical proof to support the hypothesis that turtles/tortoises can absorb any significant amount of liquid through their skins or the cloaca (or supporting tissue). In this, Veterinarians specializing in Reptiles seem to agree.

 Dr. P.M. Gibbons DVM, MS.  Notes: “There is no evidence to support the idea that reptiles might [drink] via the cloaca, though some authors have misreported the results of studies on the hypothesis” – Critical Care therapy in Reptiles 2020

C.C. Peterson & D. Greenshields.  Article:  Negative test for cloacal drinking in aquatic/semi aquatic turtles, with comments on the functions of cloacal bursae. Exp Zoo 2001; 247-254.

J.D. Martinez.  Emergency Care of Reptiles. Pract. 2007; 557-585.

J.E. Minnich.  Biology of the Reptilia.  1982 pp 325-395.

One Veterinary report even went as so far to say, “reptile skin is about as watertight as it comes”. There appears to be virtually no permeability in reptilian skin. Therefore turtles do not absorb any type of water or fluids through the skin. Fluids, including those containing any vitamin or mineral supplementation must be ingested (or injected) to be used by the turtles body for nutrition or hydration.