If interface isn't congested, traffic isn't queued in the LLQ (although it's counted against class stats), so at least on software routers, it's possible to transmit more LLQ class data then what's limited by the implicit policer. (If this is an issue, you can configure an explicit policer within the class.)
If there's no interface congestion, it's FCFS, if there's some interface congestion, tx-ring is FIFO. (NB: tx-ring overflow is what is placed into software queues.)
NB: a congested interface is one with packets waiting; different thing from "congested link" which often (incorrectly) means 100% utilization, truly congested link would be one unable to support substained offered load (i.e. exactly 100% utilization doesn't have to be congested). Also, 100% utilization doesn't have to have a congested interface, and a congestioned interface can happen with almost nil utilization.
e.g.
100 Mbps ingress; 100 Mbps egress, egress can be 100% utilized but interface can't congest
100 Mbps ingress; 10 Mbps egress, 2 packets ingress back-to-back will congest egress interface
100 Mbps ingress 10% load; 10 Mbps ingress, egress link 100% utilization, but not congested
If you have to discard egress packets, then you have a congested link
