It's possible some stain could be washed off from the rain. Most likely this won't really hurt anything, it really depends on the stain. Covering the deck with plastic might work, but this will trap some moisture and cause spotting. Check the deck stain in the morning, before the rain, and see if it is still tacky before going with the plastic. Chances are it will be dry to the touch.
For future reference; deck stains should be applied as one coat, without pooling, that soaks into the wood. A second coat can be applied after the first has weathered for a couple of months. This applies to all of the oil based deck stains that I have used.