In a mass spectrum, will the mass of the ion always be the same as the mass of the molecule?

Of course, there is NO guarantee that we observe the molecular ion. Much of the work of a spectroscopist is to ensure that his/her conditions of ionization are appropriate to generate molecular ions. For many organic molecules, this is reasonably straightforward; for inorganic molecules, not so straightforward.

As with all forms of analysis, mass spectroscopy is part of a battery of several characterization techniques. And each form of analysis should tell the same story.

Well... assuming it didn't fragment... sure. If it did, and if you are asking, "is there a molecular ion in the spectrum that shall have the same molecular mass as the original molecule?", then yes... one of them will.

But if it did fragment, and you are asking, "are all molecular ions that are produced going to have the same molecular mass as the original molecule..." then of course they would not.

Here is an example spectrum using 2-pentanone:

All of these structure fragments have molecular masses that are equal to the value indicated above the peak. Here is how the fragmentation could have happened: