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Depends how you configure it and what your clock speed is.
There is acquisition time and conversion time. You you need to account for acquisition time when changing the active ADC channel. Once that time has been allowed, then you are working with conversion time.
The acquisition time depends on source and reference resistances and temperature, the formulae are on page 185 of the datasheet. For a 2.5KΩ source resistance and internal ref, it works out around 10µs for the hold capacitor to be charged and everything to be ready.
Then...
A 10-bit conversion requires 12 TAD cycles. TAD is set in software, to one of 2,4,8,16,32 or 64 x TOSC or the internal AD RC oscillator. Also, the fastest you can allow TAD to be is 1.6µs. That alone sets a minimum conversion time of 12x1.6 = 19.2µs. TAD is set according to your clock; for example 10MHz with 16xTOSC gives exactly 1.6µs for TAD.
Doing something with the samples will take more time of course.
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