Context. The Galaxy hosts a widespread population of low-energy positrons revealed by successive generations of gamma-ray telescopes through a bright annihilation emission from the bulge region, with a fainter contribution from the inner disk. The exact origin of these particles remains currently unknown. Aims. We estimate the contribution to the annihilation signal of positrons generated in the decay of radioactive 26 Al, 56 Ni and 44 Ti. Methods. We adapted the GALPROP propagation code to simulate the transport and annihilation of radioactivity positrons in a model of our Galaxy. Using plausible source spatial distributions, we explored several possible propagation scenarios to account for the large uncertainties on the transport of ∼MeV positrons in the interstellar medium. We then compared the predicted intensity distributions to the INTEGRAL/SPI observations. Results. We obtain similar intensity distributions with small bulge-to-disk ratios, even for extreme large-scale transport prescriptions. At least half of the positrons annihilate close to their sources, even when they are allowed to travel far away. In the high-diffusion, ballistic case, up to 40% of them escape the Galaxy. In proportion, this affects bulge positrons more than disk positrons because they are injected further off the plane in a tenuous medium, while disk positrons are mostly injected in the dense molecular ring. The predicted intensity distributions are fully consistent with the observed longitudinally-extended disk-like emission, but the transport scenario cannot be strongly constrained by the current data. Conclusions. Nucleosynthesis positrons alone cannot account for the observed annihilation emission in the frame of our model. An additional component is needed to explain the strong bulge contribution, and the latter is very likely concentrated in the central regions if positrons have initial energies in the 100 keV−1 MeV range.