Not exactly. You'll still want to check on your new plantings. Unless you're getting regular heavy rainfall, the plants' roots will still need regular waterings in the spring. If you have plantings near or underneath large trees you'll want to water a little more since the tree roots are soaking up much of the water and nutrients. Also, the branches may be preventing the rain from really getting much moisture into the soil. If you have a thick layer of compost on the ground (good for you) the rain may only penetrate the first inch or two of soil leaving the roots dry.
I know you may feel silly at first standing out in the rain and running the hose, but you need to get them growing strong roots to withstand the hot, dry summer days. Two good soaks a week should do the trick-more if it's unually warm and dry. Remember, your plants are an investment. Keep them alive.