Can an S-Corp pay the sole owner/employee with a 1099?

No. S-Corp owners should be paid W2 wages and distributions. Here's a pretty good explanation as to why you can't use a 1099. Some notable quotes from the article:

IRS FS-2008-25 states that corporate officers are specifically included within the definition of an employee for FICA (Federal Insurance Contributions Act), FUTA (Federal Unemployment Tax Act) and FIT (federal income tax) withholdings under the Internal Revenue Code.

and

What many employers do not realize is that even though the “independent contractor” who is paid via a Form 1099 pays all of the self-employment, Social Security and Medicare taxes, that the payment of self-employment taxes is a different tax than payroll withholding taxes even though they are both taxed at 15.3%. Thus, the employer could still be found liable for payment of the employer and employee share of Social Security and Medicare taxes (Western Management case).