No it doesn't actually. The 'thermal mass' - strictly thermal capacity, i.e. mass times specific heat - of the masonry isn't affected by adding insulation. OK, the insulation itself has some thermal mass, but that will usually be negligible in comparison to the mass of whatever's being insulated.
- it turns the masonry into a heat reservoir
What you're trying to say is that it increases the thermal /time constant/.
Time constant of a structure = (mass * specific heat) / (U-value * area)
(First-order system approximation.)