The answer will vary by age and league. if it is youth I don't see it a problem but the board of your league (don't know why they would) may have a rule.
(Inexperienced young kid refs may take the rule literally and not let a players play with turfs. I have seen this and had to inform/educate a ref before game)
I personally would like to see all U6 players using turf rubber. Current technology sometimes does more harm the good for developing players.
As long as the turf shoes are soccer specific I don't see why a league would have a rule against it. I have a pair of Adidas Copas that are turf and I would play in those any day!
obviously soccer cleats give better traction and performance than turf so you don't see them typically. However, I played on an adult league with an older gentlemen and he had awesome vision and touch and only wore turfs...