For the reasons given above you don't want a DC offset on your drivers. Here are some Klippel measurements to help illustrate the point. If adding a protection capacitor brings the tweeter distortion back into line with what is expected that will be interesting.
Depending on the materials the suspension stiffness may loosen a bit over time. In normal use the deflection will often exceed your offset so it is hard to see a reason for concern. If you leave the amplifiers permanently on then perhaps you might have started the sagging you sometimes see in downward facing subwoofers. If the distortion levels return to what is expected then that will suggest no harm has been done.
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