Does QoS cause Router's CPU overhead?, and if it does, is it acceptable? Especially the router configured with little number of policies.
Both Narayan and David do well to caution about usage of NBAR, which, I think, emphasizes my point about what the QoS policy is actually doing. Some QoS features are much more resource intensive than others.
David's post, indirectly, touches on an issue which I didn't mention, it's possible multiple service interactions can especially degrade performance if the fast switching path reverts to software switching.
If both Narayan and David are implying, proceed with caution, they're certainly correct.
"Does QoS cause Router's CPU overhead?"
Usually, some. Especially on pure routers. (L3 switches often support their QoS features within hardware.)
"if it does, is it acceptable?"
Depends much on how busy the router is before you apply the policy and what the QoS policy is doing.
"Especially the router configured with little number of policies."
Not just an issue of number of policies, but it's often more a question of what's being done within the policy or policies.
The question of the impact of QoS configuration to the router's performance is somewhat similar to performance impact questions when adding any other services feature, e.g. ACLs.
My experience has been I've rarely seen more than an additional 5% increase to the CPU load and the benefits make it worthwhile.