The modern day potato is most definitely a different thing that any hunter gatherer may or may not have ever eaten. However this is not to say that if they did come across them they wouldn't have eaten them given the chance.
It has been shown via genetic testing that all 5000 worldwide potato varieties all come from a single origin that grew in modern day peru and northwest bolivia. It was estimated that the first domesticated potato were grown around 8000-5000 BC. This was a couple of thousand years after the first grains were planted so post agricultural revolution.
So potatos as we know them really are not a Primal/Paleo food unless they happened to have come across the original species in Peru and bolivia. So was unlikely to have played any significant part of any hunter gatherers diet.
That said should we eat them today?
As with all these questions it is very dependant on the person. So I am going to give you an argument from both sides.
Reasons against consuming potatoes are as follows. They are high on the glycemic index, so have a large effect on blood sugar spikes so are really not a good choice for people trying to lose weight or have problems with blood sugar regulation, I.e Diabetics.
Another reason is the toxic component of them, saponins or glycoalkaloids are part of the potato as a form of defence to stop animals eating them. There is some evidence to suggest that they contribute to intestinal permeability also known as leaky gut, this has connections with autoimmune responses in some people. Other negatives can come in the form of headaches, diarrhea and cramps.
Reasons to include them are they do have some good nutritional attributes, they are a good source of vitamin C and b6 and potassium. The cooking methods however very much affect the availability of these nutrients.
They also contain Resistance Starch (Starch which is resistant to digestion) which has similar benefits to fiber and helps feed the good bacteria in the gut. Cooling cooked potato helps increase resistance starch.
With all this in mind it is also important to consider in what form you may be consuming them. A baked, boiled or roasted potato is going to be much less detrimental than chips fried in vegetable oil, or a bag of crisps.
So again it it really down to where you are with your health, are you trying to lose weight, have an autoimmune condition or diabetes? Then I would suggest that they probably not going to be a great option for you. However are you at a healthy weight and in good all round health, and you don't have any of the negative effects that can come with eating potato, then you can probably get away with enjoying them from time to time.
So are they Primal?
No not really from an evolutionary perspective. The kinds available to us at the market really are modern hybrids. Although they do contain some good nutritional elements there are lots of other sources to get them from.
In summary I wouldn't suggest that they become a staple part of anyone's diet but they can be a welcome addition to those of you that don't have any of the negatives.
Keep it Primal