I would say, in most cases, the answer is No.
In fact, in many cases, a crack or two in a soundboard may have little or no effect on the tone of the instrument. It really depends on the severity of the crack(s), how many there might be, and how much separation may have occurred from the ribs underneath the board. It is this separation of the soundboard from the ribs that may cause tonal problems, including buzzing and lack of tonal production.
I have witnessed many pianos where the soundboard is riddled with cracks, yet the instrument still retains its tonal integrity because the cracks have not caused rib separation. Still, the potential is often there for separation to occur because of the crack as well.
Regardless, even if a board has both cracks and separation, it can usually still be repaired. The question then becomes whether or not a particular piano is worth the cost of these repairs, and this would be best determined by a thorough evaluation. While it may be possible to perform some stop-gap measures (pun intended!), an evaluation may be helpful to determine if your piano is a good candidate for re-building.
Obviously, if the cost of repairs exceeds the value of the instrument (sentimental value aside), then yes, it may have outlived its usefulness. But if you’re in doubt, do call a qualified tech like myself to have it looked at, and never hesitate to call me for a second opinion, either! You might not have to wave a tearful goodbye to your old faithful piano.
(photo: Baldwin SF grand soundboard showing multiple cracks. Yet, even before repairing, this piano’s tone was still vibrant and had integrity enough to not need replacing. After repairs, the piano went on to work as a solid second instrument on the concert stage.)