In our network two Domain Controllers are configured as the central (S)NTP Servers. For a switch in Layer 3 mode it is quit easy to synchronise with these (S)NTP Servers. But what is actually the best approach for access switches in layer 2 mode, that are connected to the layer 3 switch? The only IP Address they have are part of the management VLAN ID 1 which is not routable. I am actually looking for something like a broadcast without having to put a NTP Server in management vLAN.
Is your layer 3 switch the gateway for your vlans? Vlan 1 can be routed, the only restriction to this would be if you do not have any routes for vlan1. If your NTP server and layer 2 switch points their default gateway at your layer 3 switch, the layer 3 switch can route traffic across that way.
It really depends how you have the network setup and what device is handling the routing for you on the local network.