I mailed the full amount of the delinquency on the "action date." Will my case still be dismissed?

Probably. If the funds have not been posted to your case by the date the order of dismissal has been sent to the court, your case will be dismissed, even if the money comes in later. Calling the Trustee does not change the action date and will not buy you any additional time. Call your attorney as soon as you receive the Trustee's Motion to Dismiss.