Would a pressure tank do anything to water pressure without a pump?

Slowly the tank would build up pressure equal to the pressure of the artesian well. The larger the tank, the better, because it would take a while for the pressure in the tank to drop as water is used. If the tank is higher than the house, the height of the water would provide pressure.

A pressure tank without a pump might help if you have high pressure coming in with a low flow rate. It acts as a buffer tank. Will not change the average pressure but it will let you use higher pressure water longer.

Spend the money and put a pump and a tank. We do not live in the dark ages anymore.

As the name indicates, a proper pressure tank can increase the pressure in your system, which is actually helpful in many cases. Especially on the second floor. The greatest advantage to using a proper pressurized system, is the increased pump life one will gain from such a system. Using a pressure tank system is recommended for residential well systems. They do take up space and eventually need maintenance/replacement and such, just like any other system in ones house. But they are well worth it.

ASK HIM why he recommends it, and what it will do for you that your current system does not do. Then, ask if he will warranty that result, and return your money if the result doesn't occur...