Well, that doesn’t stop you from absorbing things into other parts of your body…personally I always envisioned that ability as being used like a kangaroo pouch, ie in the abdominal area. You wouldn’t be able to store anything much in your arm - there has to be somewhere for it to go - the arm doesn’t have much “squishy” area to move aside and/or compress to make room for the foreign material, except for maybe a datachip or such. Even so, anything of value like that I’d want to put in a “belly pouch” as you can cover it a lot easier with armor!
However, having an artificial arm does give you a greater benefit for hiding objects, as you can have the arm designed with such “hiding pockets”. You can even install devices into an arm, so the tradeoff might be worth it…also, since you now have a mechanical arm, it would be easier to hide such small items as datachips. With your original arm, it could be scanned up close and the chip possibly detected. With the artificial arm, it is certainly made of metal and circuitry, which would tend to provide “cammoflague” for the chip. Plus, even with a natural looking cyberskin, you can get a fake medical certificate for your prostetic arm and not draw attention from all but the most stricktest of security checkpoints.