There are two places that tagging is important, leaving out "one-armed" configurations; in the switch and on the interface itself.
The switch works by "wiring" all ports that have the same VLAN together. When a packet arrives at a port, if it is untagged, it is given the PVID as a tag. If it is already tagged and it is a "permitted" VLAN tag, it retains the tag. Depending on the specifics of the switch and its driver, if it is not a permitted tag, the packet may be dropped (I haven't seen config parameters for this behavior nor looked for it in detail). Inside the switch, if the destination MAC address is on a port that permits the VLAN, then it is sent out that port. For broadcast packets, it is sent out all ports that permit that VLAN. If the port is tagged for that VLAN, the tag is retained. If the port is untagged for that VLAN, the tag is dropped.
The interface can also have tags, each of which creates a "sub-interface" that can be accessed by the kernel, and through the kernel user-space applications. Each sub-interface "filters" to that specific VLAN, and tags outgoing packets with the VLAN. Each sub-interface (or bridge over that sub-interface) typically has its own IPv4 address, and its own set of IPv6 addresses. This allows "trunking" where one physical wire (which may be inside of the SoC or on the PCB) handles multiple subnets or streams of data. If you're only carrying one stream of data to/from a physical interface, you don't really need to use tagging as the switch's use of PVID is sufficient. Personally, when I can, I always use VLAN tags for clarity and future extensibility. That said, my network infrastructure uses many VLANs for segregation of traffic, monitoring, and firewalling.
If you tag both eth0 and eth1 to the same VLAN, that should be OK, as long as they don't have the same IP address. It's like plugging them both into the same Ethernet cable.
Most of what you describe will "work" if both the interfaces and the switch are configured properly, if you only have one stream of data to/from each of the physical interfaces.