You can call them as well and provide your Hunter Ed# and they can unlock your account rather than snail mailing in the documentation.
Last year I didn't draw the preferred zone/season I was after but still grabbed a left over tag in the season prior to what I had applied for and still had a successful hunt. Iowa has a healthy turkey population and a limit of 1 bird. Their first and second season often has snow on the ground and really cold temps but I lucked out and caught beautiful weather in the second season and many turkeys gobbling.
If you're set on certain dates in a certain area, it may take you two years to get the tag, but if you have options then I would recommend grabbing a leftover tag if you don't draw and still getting out there this spring.