If I have some interface, like ether1, and a bunch of VLAN interfaces on it, like vlan2 and vlan3, does ether1's IP address "carry over" to the VLANs?
No, IP address is bound to
interface. In your case ether1 is interface for untagged frames passing ether1
port. For VLAN interfaces ether1 is simply underlying hardware
port.
One should not forget that ROS, being Routing OS, will gladly
route packets between different interfaces (including ether1 and associated vlanX interfaces). If traffic between these interfaces is not desired, one can configure firewall rules to block it.