Can't really speak for admissions, but "dramatic improvement" to me means the applicant has work hard to get better and it should be a plus. While standard test scores are important, they are only one of many factors that admissions consider.
If you haven't yet, check out the recent posts (within this year) by Just Dad, Cerberi and many others on how to improve on SAT and ACT.
For HS Juniors and younger students, I recommend prepare to start taking your SAT/ACT during fall/winter of your Junior Year. You are likely either a) have time on your side to improve, or b) do well enough early and check it off your To Do list BEFORE your Senior Year. Don't forget to account for the unexpected (e.g. test postponed due to winter weather) and how that may affect your plans.
Agree with others that it is "easier" to request the results to be sent for free during the test, but I do not believe it is necessarily the "better" option for reasons I stated above.