No. The Centers for Disease Control and Prevention (CDC,1), the American Dental Association (ADA,2), OSAP(3), most state dental licensing boards, and dental handpiece manufacturers all recommend heat sterilization between patient uses. Virtually all handpieces currently in production are heat-tolerant, and those that are not can be retrofitted to allow heat-processing. Autoclaving and chemical vapor sterilization are considered accepted methods of heat sterilization. High-level disinfection via chemical germicides cannot be biologically monitored to assure sterility. Further, extended contact with chemical germicides may corrode handpiece components.
References:

(1) CDC. Recommended Infection Control Practices for Dentistry. MMWR Morbid Mortal Weekly Rep 1993;42(RR-8):1-14. Available at http://www.cdc.gov/mmwr/preview/mmwrhtml/00021095.htm
(2) ADA Council on Scientific Affairs and ADA Council on Dental Practices. Infection Control Recommendations for the Dental Office and Dental Laboratory. J Am Dent Assoc 1996;127:672-680.
(3) OSAP. Infection Control for Dentistry Guidelines , September 1997. 

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