I'll stick my neck out and say that he's going to be in the majors in September even if the not with the Nats. He's just a deadly runner and his D is very good. He is not a well rounded player, but he's more or less a specialist. You say "until MLB starts using Designated Runners," but they've done it for ages. Dave Roberts was a legit ballplayer, but his most famous role was strictly as a pinch runner. The names Quintin Berry and Terrence Gore have come up. They always managed to find a spot on 25 man rosters down the stretch as specialists. With a 26 man, it's a lot easier.
Nunez runs fast. So did Herb Washington, who was an NCAA sprint champion, and who tied or broke the world record several times in the 50- and 60-yard dashes. Finley signed him as a dedicated runner, but gave him up after a season.
Who were Quintin Berry and Terrence Gore? I looked them up, finding that one of then had a good rookie season, but later played in 13, 10, 8, and 7 games, each with a different team. If he was worth a roster spot, some team would have kept him a second year. Gore once stole 11 bases and once stole 13. That's so little that he accumulated .1 WAR, while Berry was rated about -5.
How often have the Nats found a use for Nunez this season? Nunez has gotten into 14 games, scored 5 runs and stolen 2 bases -- caught once. Nunez has contributed nothing. I was a Yankee fan for most of those seasons after Bob Shorted Washington, and while MLB gave expansion franchises to small cities like Miami, Tampa, and the rest. I watched more than a few World Championship teams, and Yankee teams that went to the playoffs. Also some Met teams. I can't remember either team bringing up a guy just to run fast in October.
If Nunez goes back to Miami, will they just dump him again? Where would they use him?