Bottom line: There is no direct clinical evidence that use of alkalinized fluids is effective at reducing renal damage.
Summary: The DynaMed article on Rhabdomyolysis (see Treatment>Fluid and Electrolytes) states that use of bicarbonate is controversial lacking directing evidence. references an exchange about an NEJM paper N Engl J Med 2009; 361:1411-1413) where the author reply reiterates that there is little clinical evidence of effectiveness of bicarbonate. The authors of the NEJM paper do indicate that some investigators have used bicarbonate solutions in managing rhabdomyolysis, (endpoint was percentage of circulating myoglobin eliminated), but comparative studies cited (in Table 4) did not demonstrate a clinical benefit to use of bicarbonate.
A recent systematic review (Ann Pharmacother. 2013 Jan;47(1):90-105. doi: 10.1345/aph.1R215. Epub 2013 Jan 16. Prevention of kidney injury following rhabdomyolysis: a systematic review. Scharman EJ, et al.)
This systematic review corroborates DynaMed and the NEJM paper. It reports several case series and retrospective cohort studies cited in the NEJM paper. The largest was a retrospective study of a subgroup of 382 patients with rhabdomyolysis and serum creatinine > 5000 U/L. 154 (40%) also received bicarbonate and mannitol in addition to normal saline (NS), compared to 228 (60%) who received NS only. RESULTS: Rates of acute renal failure were 22% (bicarbonate + mannitol) vs 18% (NS only), p =0.27. The two other smaller retrospective cohort studies reported similar findings. See pp. 99-10 of the systematic review for details.
Finally, a recent review (Nature Reviews Nephrology 7, 416-422 (July 2011)) explains (in the Historical Overview section) that the use of bicarbonate was based on experiments demonstrating that myoglobinuria was associated with nephrotoxic effects when the urine was acidic but not when it was alkaline.