Does the Many Worlds interpretation of quantum mechanics necessarily imply every world exist?

No, it doesn't. For example, since charge is conserved, every "world" in the wavefunction must have the same charge. This goes for any other conserved quantity, too.

(This doesn't rule out you being a rockstar, though.)

The crucial word is "interpretation".

In physics it means that the results of calculations, hard numbers to be checked with data for interactions and processes that we can measure in the lab, are the same in all interpretations of a theory.

There is no difference in the hard data.

One can see the integrals as "many worlds splitting off", but it is just mathematics; going further than that it is metaphysics, not physics.

I will give an example:

Take an apple. One can fit it with a fourier series in three dimensions. The series has an infinity of terms with sines and cosines and the sum of the terms gives the apple's shape. Is the apple full of sines and cosines? One could make an interpretation that each term is real and exists in some space, coming together to make the apple.

Any alternate present must be the result of a whole possible alternate history. Assuming our decision making is not sensitive to quantum effects in our rather noisy brains (and you did not make your career choice as a random outcome of a quantum experiment, with rockstar already being on the table), significant alterations might be necessary to make rockstar-you happen. The alternate-reality person might be rather different from present you. There also might be careers that are unavailable in any history, though I have no idea how one would go about proving such a thing.