For coaches yes they will. Patriots resigned their coach and another team also signed their coach again after they were eliminated from the playoffs. If you're talking about resigning their players you will need to go into the settings for each owner or coach and set it so the cpu will handle the resign.
I know Fisher and another high profile coach got fired and I was trying to get Fisher for my team but another team outbid me. Next time I start it up I'll check which coaches went where and will report back.