Do DSL / ADSL modems have an ADC with ~ 2 MHz sampling rate?
They have a much faster ADCs. Also, ADSL2+ has its downlink up to maybe 2.2 MHz, so you'd need at least 4.4 MS/s to do that.
In reality, single-digit MHz ADCs are &quot;old tech&quot; and relatively cheap. Together with it being desirable to oversample the signal to apply digital filtering to increase your SNR, I'd presume that modern (as in: of the last 20 years!) ADSL modems have &gt; 5 MS/s ADCs.
You'll probably not find a separate ADC on the board – typically, these things are integrated into AFE (analog front-end) ICs, integrating both ADC as well as DAC and a fair bit of analog and digital signal conditioning, and usually things like digital downconversion, sometimes clock recovery.
Such chips make highly-integrated and cheap DSL modems possible, but also make these devices less useful as general-purpose ADCs.
Also, because you ask like that, and because people will wonder anyway: No. This is not a clever way to circumvent export restrictions / technology embargoes. Officials in charge of export control aren't stupid, and companies want to sell millions of chips for DSL modems everywhere, so I'd assume it'll be practically impossible for the average engineer to convert these to general purpose ADCs/DACs.