Well, can't deny that a good number of areas have been too dry this year, so far. But to more directly answer your question, yes, there is such a thing as too much rain for pepper plants. Whether your plants are in the ground or in pots will make a difference. If they're in the ground, there's typically more "wiggle room" before the plants start having problems, simply because the rain will dissipate into the ground - there's more area for it to disperse into. This doesn't make the plants exempt from possibly getting too much rain, it just means it will be less likely to occur.
With pots, it's important to have sufficient and large enough drain holes, but even with this it can get to be problematic. Last year here was a good example. We had a pretty dry summer, but then as we swung into the Fall, the rain started, and just didn't seem to stop. I'm not talking a mere 3 days worth, either, but weeks of it. It didn't necessarily pour down, but just didn't really stop, either. What happened to my plants (I grow in pots)? The ones I couldn't move into a spot to shelter from the rain first started turning yellow. This is caused by excessive nitrogen. Plants generally love rain water best because of the nitrogen, but there really is such a thing as too much of a good thing. And yes, this can happen to plants in the ground as well, if they have sustained rain like we had.
The second thing that happened seemed to depend upon the variety of pepper. The Congo Trinidads were the worse of my plants for this. The plants actually uptook so much water, it caused the pods to start splitting open. Generally they split in a rather up-and-down manner, from stem end to blossom end, but sometimes they split horizontally, too.
Three days isn't all that bad. Your plants may begin to yellow a tad, but as long as they ultimately dry out they'll be fine. If it keeps raining, though, you should really consider doing something to shelter them.