Not much is known on the effect of the form of the interparticle interaction on the possibility of off-diagonal long-range order (ODLRO) for bosons on a continuum in the solid phase. It is known that systems with a model interaction suitable for 4He do not have ODLRO in the ideal commensurate crystalline state. Here we study the case of a soft-core system, where particles interact with the two-dimensional screened Coulomb potential. The system is studied at T=0 K with the exact shadow path-integral ground state (SPIGS) Monte Carlo method. We find that no ODLRO is present in the ideal commensurate crystalline state. We study also the defected crystal, containing few vacancies or interstitials. We find that at low density the formation energies of vacancies and interstitials are very close, while at high density interstitials have a smaller formation energy. Both vacancies and interstitials are shown to be able to induce ODLRO in the crystal.