It is parallel in the sense that you can decode 4-6 instructions in parallel, yes. It is not parallel in the sense that variable length decoding requires each of your decoders to talk to the other ones to coordinate on instruction length boundaries, which means there is going to be a lot of serial logic in your decoder circuit.

It doesn't, if your L1$ predecodes at fill time and stores instruction length.

Something, somewhere does have to do a serial length decoding of course. But when you look at the L2 access latency and throughput (which is the minimum L1 fill latency), it's clear you could afford to do that part of the decode over more cycles.

New designs are not just predecoding lengths but entire uops now into the first level instruction cache which is the same concept they just call it a L0 and L1 rather than L1 and L2.