In my personal experiences with my hair, the answer would be no. I think it can be different for every person though. When I have had damage that I didn't get rid of, my hair would just break for me and my hair would stay the same length for months, years even. My specific case in point for me was my transition time- with 7 inches of starting hair and trims ~6-8 weeks apart I chopped my last 2-3 inches at 10 months. In November of 2013, I was 11 months post mini-big chop, and was trimming every 3-4 months. I had not gotten back to my 7 inches yet- I even lost almost an inch between October and November. Then I lost more when I trimmed all the wonky ends I noticed at the time off. Since then I've been CG, using protein, and trimming anywhere from every 4-8 weeks. I've actually gotten back all of the length that I lost already even with losing about an eighth of an inch each time I trim.

That being said, I also think that trim frequency will vary widely from person to person for ultimate growth, and even within different parts of your head. I'm noticing lately that my crown area and the area that is where I lay on when I lay on my back need trims more often than other places on my head. They get really tangly no matter what, and rough feeling sooner than other hair areas.
3C/4A, fine texture, low-medium density, and low porosity
CG since November 2013.

Pre-Poo: infrequent now, Coconut Oil overnight
Shampoo: Curls unleashed/for occasional sulfate wash when needed, everlasting sunshine.
Conditioner: Suave Naturals Everlasting Sunshine and GVP's conditioning balm.
Styler: iagirl's flaxseed curl cream or gelatin gel/conditioner mix. <3
PT: iagirl's gelatin treatment 3-4 times a month, with conditioner/honey/avj