Not a chance. It was not uncommon for half a team to be between 5'7 and 5'9. No amount of "equipment" or "training" would normalize the disadvantages this would put them in in the modern era. A few of these smaller players would squeak through, but only a few.
Someone like Robinson would be a lock, however.
Just out of curiosity I took a look at the four playoff teams who made the playoffs in the final year before the '67 expansion: Toronto, Montreal, New York & Chicago. Players 5'9" & under. It's a pretty impressive list (I excluded players that played less than 20 games):
The Skaters:
Dave Keon, Ron Ellis, Bob Baun, Henri Richard, Yvan Cournoyer, Claude Provost, Dick Duff, Rod Gilbert, Bernie Geoffrion, Reggie Fleming, Bill Hicke, Stan Mikita, Pat Stapleton, Kenny Wharram, Lou Angotti, Wally Boyer
The Goalies: Bruce Gamble, Charlie Hodge, Gump Worsley, Rogie Vachon, Charlie Hodge, Denis DeJordy
I wholeheartedly agree that a smaller skater has more of an uphill battle to stick. They'd better have good wheels & above-average skill. That said I didn't find that there were ANY teams with 1/2 their players under 5'9", usually there were only a handful per team. Conversely, most teams from the era had few players over 6'1". Mostly, as is the case today, they were made up of players within the average height range. What's missing is the behemoths of today. There aren't any comparables to Chara of course but also thankfully no John Scott's either. The above list includes 8 HOFers (yes, I know Duff is questioned, but Vachon and Provost are continually cited as players who should probably be in, so call it a wash). Now compare that list to this one from a couple of years ago on the tallest players in the league:
http://www.sportingcharts.com/articles/nhl/tallest-players-in-the-nhl.aspx
There's Chara and Pronger, surefire HOFers, and a few decent players like Gill, Boyle, Bishop, Antropov, maybe Myers if he turns it around. I'm not sure who you'd argue from this list of O6 era undersized players would "squeak through" but there's certainly a helluva lot more skill & hockey sense in the former list than the later.
I agree on Robinson. Not many big men who could skate and had skills like Big Bird.