This is entirely dependent on the program you are applying to.
Some programs are flexible with deadlines, particularly so if applicants are domestic students. Others, as pointed out are very strict. There may be some of both types of programs within the same university or even college.
You can always try and the worst that can happen is you're told no. For example, a few options:
- Call or Email the admissions staff or the director of graduate programs and let them know you're taking the exam on DD-MM-YYYY. Ask if they will consider you for a provisional admission that's conditional on you obtaining a competitive score.
- Just apply anyway with what you have. Incomplete applications rarely move into the decision process. Execute #1 as well.
Again, this is very program and personality-dependent so your chances of success will vary greatly depending on the situation.* Some programs consider your best GRE score. Some super score (take best from each category).
* And how far "off the mark" your GRE scores are currently.