I'm not sure what you mean about doing terrible the first time and then intentionally improving. I don't think most parents want to pay for multiple testings and most students don't want to give up a Saturday morning if they could do well the first time.
After following this board for many years, I can tell you that while I can't statistically prove that repeat testing improves scores, it appears that it is so. Experience does help, particularly with the ACT. It is a given strategy that has appeared on the Parents Board multiple times that students should start with the ACT, probably around spring of 10th grade. In order to make sure that score remains totally private, not only should students not send it to any colleges, but the high school information should be omitted as well. Some high schools place the stickers on transcripts and the information is provided to colleges in that manner. If the student does well and chooses to provide that score, the additional fee can be paid at that time.
More and more schools are giving the ACT the same consideration as the SAT, particularly if the student lives in an area where the ACT is the dominant test. Since the SAT record is cumulative and there is no way to omit poor performance, it only makes sense to start with the ACT to see how the student performs on standardized testing.
D took the ACT in the spring of her 10th grade year and repeated during junior year and senior year in the fall. Her last score, the score officially reported to Vanderbilt, was 6 points higher. Her sophomore score was reported on the hs transcript (I hadn't figured out the omit the hs info part yet). In the information session I attended with S, Vandy admissions noted that they viewed the ACT as a whole (the composite), not by parts like the SAT. Although the testing formats for both have changes, I think this continues to be true.