Here's some evidence suggesting that Martin will have a very difficult time breaking the record --
Martin has played 10 seasons and has 13,366 yards (third-best all-time after 10 seasons, behind only Barry Sanders' 15,269 and Emmitt's 13,963, and just ahead of Walter Payton's 13,309). Martin just completed the best 10th season in NFL history, 1,697 yards, breaking Payton's record of 1,684.
The best 11th season in NFL history belongs to Payton -- 1,551 yards. Nobody else is within 300 yards of that. (Emmitt is second at 1,203.)
The best 12th season in NFL history belongs to John Riggins -- 1,347 yards. Only Payton's 1,333 is within 300 yards of that. (Emmitt is fourth at 1,021.)
The best 13th season in NFL history also belongs to Riggins -- 1,239 yards. Nobody else is within 250 yards of that. (Emmitt is second at 975.)
The best 14th season in NFL history belongs to Marcus Allen -- 890 yards. Nobody else is within 200 yards of that. (Emmitt had 256.)
So, even if Martin matched the best 11th season, the best 12th season, the best 13th season AND the best 14th season in NFL history (at which point he'd be 35 years old), he'd still have only 18,393 yards -- just 38 yards more than Emmitt's record. If he falls short in any season, he'll almost certainly fall short of the record.
Martin has the disadvantage of being a year older than Emmitt and Payton at the same stage of their careers, and the other two running backs whom he has to match (Riggins and Allen) didn't have anywhere close to the wear and tear in their first 10 seasons as Martin (or Emmitt). Riggins averaged only 185 carries in his first 11 seasons, and Allen averaged only 191 carries in his first 13 seasons. Martin has averaged 330.
If Martin can manage to be that successful in his 11th, 12th, 13th 14th and/or 15th seasons AND match or break Emmitt's records for consecutive seasons as a feature back (13), total seasons as a feature back (14) and career rushing attempts (he almost certainly would have to, since his average per carry is lower than Emmitt's), all while being a year older than the man he's chasing, then he would deserve to hold the record. But I just don't see him even coming close.