If you're referring to the 1863 campaign waged by Col. Christopher "Kit" Carson, then it is possible but unlikely. Carson's scorched-earth campaign began on July 7th, 1863. (http://www.history.com/this-day-in-history/kit-carsons-campaign-against-the-indians) Sherman's Savannah campaign began when he cut supply lines and communication with the Union on November 15th, 1864. (https://www.civilwar.org/learn/articles/scorched-earth) Given this time span, the distance between New Mexico and the Eastern Theater, and the fact that Grant was in command of the Western Theatre until 1864, it is unlikely that Sherman would have known about the campaign and even if he had known about it, it likely wouldn't have impacted his strategic decisions. Scorched-earth only entered military nomenclature during WWII (https://www.merriam-webster.com/dictionary/scorched-earth), however the tactic itself is ancient. The earliest recorded use was by the Scythians to halt the invasion of Darius I in approximately 513 BCE. (https://www.metmuseum.org/pubs/bulletins/1/pdf/3269235.pdf.bannered.pdf) It is more likely that both Carson and Sherman simply used a common tactic in response similar conditions.
There were Navajo holdouts, and in August 1864 Captain John Thompson and 35 men of the 1st New Mexico Cavalry re-entered Canyon de Chelly. In his report on that expedition after returning to Fort Canby (formerly Fort Defiance) in Arizona Territory, Thompson said he had systematically destroyed more than 3,000 mature peach trees. On one day alone, he reported, he cut down 500 “of the best peach trees I have ever seen in the country, every one of them bearing fruit.” But he had not laid waste to all of them, because later that year Captain Edward Butler, the commander of Fort Wingate in New Mexico Territory, reportedly destroyed another 1,000 of the Navajos’ prize Canyon de Chelly peach trees.
—to wit with—
Sherman's March to the Sea, more formally known as the Savannah Campaign, was a military campaign of the American Civil War conducted through Georgia from November 15 to December 21, 1864 by Maj. Gen. William Tecumseh Sherman of the Union Army.
It is possible.