First,
A triplex pump needs no pulsation dampener, unless you have a device like a pulse pump attached to the main pump, which will induce pulsation as it inhibits one of the cylinders.
Second, the simple lack of a pulsation dampener is not enough to cause visible or felt pulsation if the system otherwise dampens the pulsation with the system hoses acting to quell it.
However, if your unit is indeed equipped with a pulse pump for last step chemical injection, a pulse dampener will at the very least aid chemical injection as it reduces pressure spiking(pulsation) that would inhibit the re-introduction of the chemical downstream.
BTW, some TM systems lack a "visible" pulsation dampener, but actually have what is known as a pulse hose or "throbber" hose on the outlet of the pump, which performs the same function by expanding and contracting, thus smoothing out the flow.
