Can I provide a negative input voltage to this (or any) ADC?
The ADC operates on a single supply, meaning \$V_{SS}\$ is ground, and \$V_{DD}\$ the positive supply. The datasheet lists under AMR (Absolute Maximum Ratings) that no voltage should ever be lower than \$V_{SS} - 0.3V\$. Note that AMR are indeed Absolute Maximum, and that you're not supposed to operate the device at the given limits.  

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The \$\pm\$2.048V mentioned in the datasheet is differential, meaning that \$V_{IN+} - V_{IN-}\$ can range between -2.048V (like \$V_{IN+}\$ = 0V and \$V_{IN-}\$ = +2.048V) and +2.048V (like \$V_{IN+}\$ = +2.048V and \$V_{IN-}\$ = 0V). So the differential voltage can be negative while both input are positive.