For local stuff, yes.
HOWEVER, states would be required to keep two separate election rolls, which is a reason why the 26th Amendment (lowering voting age from 21 to 18) exists. From Wikipedia:
Oregon v. Mitchell
During debate of the 1970 extension of the Voting Rights Act, Senator Ted Kennedy argued that the Equal Protection Clause of the Fourteenth Amendment allowed Congress to pass national legislation lowering the voting age.[17] In Katzenbach v. Morgan (1966), the Supreme Court had ruled that if Congress acts to enforce the 14th Amendment by passing a law declaring that a type of state law discriminates against a certain class of persons, the Supreme Court will let the law stand if the justices can "perceive a basis" for Congress's actions.[18]
President Nixon disagreed with Kennedy in a letter to the Speaker of the House and the House minority and majority leaders, asserting that the issue is not whether the voting age should be lowered, but how. In his own interpretation of Katzenbach, Nixon argued that to include age as something discriminatory would be too big of a stretch and voiced concerns that the damage of a Supreme Court decision to overturn the Voting Rights Act could be disastrous.[19]
In Oregon v. Mitchell (1970), the Supreme Court considered whether the voting-age provisions Congress added to the Voting Rights Act in 1970 were constitutional. The Court struck down the provisions that established 18 as the voting age in state and local elections. However, the Court upheld the provision establishing the voting age as 18 in federal elections. The Court was deeply divided in this case, and a majority of justices did not agree on a rationale for the holding.[20][21]
The decision resulted in states being able to maintain 21 as the voting age in state and local elections, but being required to establish separate voter rolls so that voters between 18 and 21 years old could vote in federal elections.[22]
...
James J. Kilpatrick, a political columnist, asserted that the states were "extorted" into ratifying the Twenty-sixth Amendment.[27] In his article, he claims that by passing the 1970 extension to the Voting Rights Act, Congress effectively forced the States to ratify the amendment lest they be forced to financially and bureaucratically cope with maintaining two voting registers.
