Nope. It'll be 2032 before they control their first round pick. But at least they are old, bad, and expensive in the meantime, so there's that.
https://arizonasports.com/nba/phoenix-suns/future-picks/3572960/
Where are the Suns slated to pick in future drafts?
2025: Least favorable first-round pick between Cleveland Cavaliers and Minnesota Timberwolves (projected to be No. 29); least favorable second-round pick between Denver Nuggets and Philadelphia 76ers (projected to land at No. 54)
2026: Least favorable first-round pick between Phoenix, Orlando Magic, Memphis Grizzlies and Washington Wizards; least favorable second-round pick between Golden State and Denver (via Charlotte)
2027: Least favorable first-round pick between Cleveland, Minnesota and Utah Jazz; no second-round pick
2028: Least favorable first-round pick between Phoenix, Washington, Brooklyn Nets and Philadelphia 76ers; second-round pick via Boston Celtics (if it lands between Nos. 46-60)
2029: Least favorable first-round pick between Cleveland, Minnesota and Utah; no second-round pick
2030: Least favorable first-round pick between Phoenix, Washington and Memphis; no second-round pick
2031: No first-round pick (traded to Utah Jazz for 2025, 2027, 2029 first-round picks); no second-round pick.