You can decline the distance penalty for any foul so the answer to the question is yes you can decline a dead ball foul however that does not change the down since the play did not actually start. Lets say that you have a fourth and 10 and the offense has a false start. You can decline the yardage. The only time that I have seen this is when a team is punting and they want a little more room to put a team deep in their own territory.

VHSLhelper there is only one situation that I can think of off hand that would have a penalty automatically declined and that is when a team intercepts or recovers a fumble for a TD. If the team that fumbles or throws the interception fouls before the turnover the foul is automatically declined because the result of the play is a Touchdown.