Michael,

A seat assignment does not guarantee you from being denied boarding. However, in most cases if there is a need for involuntary denied boarding, the policy is as follows, per Spirit's Contract of Carriage (available on spiritair.com):

If a flight is oversold and there are not enough volunteers, other customers may be denied boarding involuntarily in accordance with the following:
8.2.1. The last customer(s) to check in may be denied boarding in the event of an oversell, however Spirit reserves the right to determine the manner of priority per 14 C.F.R. Section 250.3.

If you decide to pass on a seat assignment, you'll be provided with a seat assignment at no charge when you check-in (up to 24 hours prior to your flight at spiritair.com).