No, in principle the initial values do not vary. The embryo, once implanted, initiates the release of the beta-hCG hormone, regardless of the site of implantation.
However, the evolution of the hormone value may vary, since in an ectopic pregnancy there will come a time when the embryo stops its development and this blocks the release of the beta-hCG hormone, which will progressively decrease its level in the maternal blood.
Therefore, although initially, the beta-hCG test would not be helpful in detecting ectopic pregnancy, at a more advanced stage, it can be important.