Honestly it doesn't look optimistic. There's a lot of laugh on MTF that D'Joke is a one-slam wonder and Butt-head won't win any slam in the future. They were Top 100 players in the age of Harrison though. Generally there's a tendency that Grand Slam winners are in the Top 100 at the age of 18. Harrison is outside Top 200 and hardcourt season in America - the most favorable for him - behind his back...
This is true, but times they are a changing. Harrison is the second youngest player in the top 250:
Rank Player Age
229 - Bernard Tomic (AUS) 17 Years, 10 Months, 18 Days
220 - Ryan Harrison (USA) 18 Years, 04 Months, 01 Days
224 - Filip Krajinovic (SRB) 18 Years, 06 Months, 12 Days
184 - Grigor Dimitrov (BUL) 19 Years, 03 Months, 23 Days
The youngest player in the top 100 is already 21. I think if Harrison makes it to the top 100 before turning 20 (looking a good chance), he is well on track to be a top player. Grand Slam champion is another thing and it's too early to tell for that in my opinion. However, taking all players born 1989 or after, he is right up there among the very best.