For AC voltages, the DAQ would continue measuring, and you would see the AC waveform coming through in the data (assuming that the sample rate is high enough to measure it).
An AC voltage itself will not cause damage, assuming that the voltages are still within the ratings of your DAQ. You've expressed that the voltage range of your DAQ is 0-10V. Therefore it can handle any AC or DC signal that remains in that range.
If you applied directly to the DAQ a 1v amplitude AC voltage with a DC offset of 0v, the range of the AC would be -1v to +1v. This would be outside the range for your DAQ for the negative half of the waveform. But if you had a 1v amplitude AC voltage with a DC offset of 5v, then now the range is (+4v to +6v), so the voltage is always staying within the range.
So with your divider you can already handle any AC waveform that stays within the 0v-30v range,
Note: If you are using the USB-6009, then this system can measure negative voltages, and actually can go from -10v to +10v.