As you likely know, the SAT/ACT requires a significant time commitment. For this reason, under ideal circumstances, you won’t have to complete most of the application process while simultaneously studying for the SAT/ACT. Instead, try to get the SAT/ACT out of the way early (during your junior year). Then, you can focus on the majority of the application without having to worry about SAT/ACT prep.
However, if you end up taking the SAT/ACT in the fall of your senior year, you may choose to complete some of the application process as a break from your SAT/ACT studying.
You will have a few weeks between taking the SAT/ACT and receiving your score, so you may use this time to finalize your applications. However, you’ll likely want to take a break from anything application-related for at least a few days or even up to a week after taking such an important standardized test. Aside from wanting to relax in its aftermath, you’ll probably have neglected many of your non-admission-related obligations (work, school, family, friends, etc.). Once you receive your score, you may want to apply as quickly as possible in order to apply Early Action or Early Decision, depending upon the school.
Note: colleges will not look at your application until it is complete – meaning they have received all required components, including your SAT score. Even if every other part is in, they won’t look at it if they don’t have that magical number. Why? Because, while they’ll (probably) look at all the other parts, the test score is one of the most important factors in determining whether they’ll admit you. They won’t waste their time reading the college essay, etc., if they don’t know whether you scored well or poorly.