Colleges will generally consider your SAT / ACT scores if the college receives that score a little bit later after the application deadline. This is true amongst many colleges and has been the practice for many years.
For example, Purdue explicitly says  about the November 1st, 2016 deadline that:
Encourage your students to send their
spring 2016 test scores to Purdue to
ensure that their application is
complete by November 1. Fall scores
will “catch up” with applications and
will be used for admission and
scholarship decisions once they
arrive, but for scholarship and Honors
College consideration, it is important
that students not miss the November 1
deadline. Test scores must be sent
directly from the testing agency; we
do not accept test scores on school
My interpretation if this is that:
- You must finish your application by November 1st.
- However, the scores can arrive later.
- Your SAT / ACT scores must be from a fall administration (e.g. anytime December 20th or before). Your scores must be sent directly to the college.
Of course, to be 100% sure, the best thing to do is always to call the school.
The general lesson here is that the deadline for YOU is not the same as the deadline for the SAT / ACT, or even the teachers writing your recommendation letters. Deadlines not for you tend to be later, but generally even these need to get to the school 3-4 weeks+ (rule of thumb) before they announce the decision.
- Past experience applying to bachelor and PhD Programs.
- Conversations with admissions officers.