It depends what you mean by absolute encoder. If you mean the old style, low resolution ones that just use any standard inputs and take a ton of wires then yes all PLCs can. Productivity and BRX PLCs even have instruction inputs for them so you don't have to manually code the logic in.

If you mean modern absolute encoders that are high resolution and interface with SSI, BiSS C, or even EtherCat then no, none of the AD PLCs can use those. I asked years ago and was told the product request had been submitted but haven't seen anything since then. It would be nice if they supported these with a 22-bit absolute input module

You can however use one of the more rare and slower responding EtherNet/IP absolute encoders, and have it be a simple implicit input device. Productivity and BRX both support EtherNet/IP.

The interesting thing is the SureServo2 line uses high resolution absolute encoders (2 million ppr/21-bit) as their input for the motor position. So technically AD has a product with these types of encoders built in. The servos are made by Delta though, and maybe Automation Direct doesn't actually have anything to do with the firmware and implementation of these, IDK. Judging by the other motion products Delta makes, I make the assumption that the built in ABS encoder in the servos likely communicates to the servo drive with EtherCat.

Edit: I actually just remembered that AD does carry a few Lika brand encoders, including EtherNet/IP ones. They arent the best, as they are only 13-bit, but you can get them from Automation Direct and they are cheaper than other brands with their higher resolution.

https://www.automationdirect.com/adc/shopping/catalog/sensors_-z-_encoders/encoders/rotary_encoders/am59h-1314-ep15-m12

If using a "modern" SSI absolute encoders, there are gateways and converters available.

An example of SSI-to-Ethernet/IP gateway:

https://www.likausa.com/news/ssi-to-ethernetip-gateway-now-possible/

An example of SSI-to-analog converter:

https://www.pepperl-fuchs.com/en/products-gp25581/99830