Can concentrated sulphuric acid react with copper turnings?

The answer is of course true.

Copper metal and concentrated sulphuric acid undergo redox reaction.
Cu(s) + 2H2SO4(l) --->(heat) CuSO4(s) + SO2(g) + 2H2O(g)
The copper turnings dissolve. Colourless gas with a pungent choking smell of burning sulphur evolves, which can decolorize acidified potassium permanganate solution.
Steam is also given out.

Copper salts react with concentrated sulphuric acid in a similar way as other salt-acid reactions, e.g.
CuO + H2SO4 ---> CuSO4 + H2O
Cu(OH)2 + H2SO4 ---> CuSO4 + 2H2O
CuCO3 + H2SO4 ---> CuSO4 + H2O + CO2
Cu(HCO3)2 + H2SO4 ---> CuSO4 + 2H2O + 2CO2

It should be noted that CuSO4 does not react with H2SO4