That said, the unequivocal answer is "yes" – router queue length can seriously affect performance in unexpected ways. The most typical is when queues are too large and the result can be dramatic increases in RTT/jitter, and sometimes destabilized TCP flows.
However, you seem to be referring to output queue lengths on the server interfaces, as opposed to input queues on a router. This I am less sure of since it sounds like something above Layer 3 and therefore part of the OS. And I can easily imagine that it is a symptom of something in the network.
I would need more details though. If you care to write back, I'll try to help further.
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