If a person has a pistol and an attachable shoulder stock, does this constitute possession of an NFA firearm?

Yes, unless the barrel of the pistol is at least 16 inches in length (and the overall length of the firearm with stock attached is at least 26 inches). However, certain stocked handguns, such as original semiautomatic Mauser “Broomhandles” and Lugers, have been removed from the purview of the NFA as collectors’ items.

[26 U.S.C. 5845, 27 CFR 479.11]

Source ATF: https://www.atf.gov/firearms/qa/if-person-has-pistol-and-attachable-shoulder-stock-does-constitute-possession-nfa