YES, YES, YES, YES, YES!!!!!!!! My cousin and her boyfriend both did those Spring Break mission trips to South America once and the schools they applied to were ecstatic about that on their resume. Her boyfriend did a couple of them and the PA schools loved it on his resume. It was something that stood out. Even if you did it when you were 12 to 14 years old (or so) it still shows a passionate and holistic side of you. I did Habitat for Humanity for two weeks my senior year of HS and that is still on my resume because it humanizes my resume. I know there is a difference between the Mormon Missionary Trips and the stuff I am listing, but yours was two years of dedication to helping others.
I know people who take a year off from undergrad to med school and they do City Work in Detroit or Chicago to teach underprivileged kids for a year. They didn't take any courses to raise their GPA, didn't retake the MCAT, but that extra year of service WOWED the admissions committees.
Some how I would possibly incorporate it into your personal statement because if you just put it in your resume they may just glance by it and forget about it, but if you put it in your personal statement it will show more about how it helped you as a person. If you still are in good contact with the mission trip leader it can't hurt to ask for a Letter of Recommendation from them as an additional letter after you receive a letter from two teachers and one DPM. For the AACPMAS application it will ask for "Professional Experience>>>Health Care Experience" but I don't think this counts so really just putting it on your resume and/or personal statement is the only way to go.