It is unlikely. Pickups are wire wrapped around magnets which are a lot tougher than active electronics. If they get too hot they could melt or short windings. Surges in the electrical systems usually kill active electronics though.
What kind of pickups are they? Can you measure their resistances with an ohm meter? (You may have to unsolder the hot leads heading into the pots to make the resistance measurements). If the resistance measurements check out, you are OK.
If both pickups sound the same volume wise, there is probably nothing wrong with the pickups. The liklihood of both of them failing the same way is not high.
Dave