Question about Cisco QoS

I've never had to worry about QoS before, so i'm not really familiar with it. Default has always worked for us in the past. But we're now deploying a bunch of non-cisco phones and i've been told i need to put new QoS policies on our switches to make Cisco trust their dscp markings.

My question is when i put these policies out and add them to the switch interfaces that have the non-cisco devices attached, do i have to worry about anything in between that doesn't actually have the phones directly connected, but is just passing the traffic along? I'm assuming, possibly incorrectly, that once the traffic is trusted and prioritized on the interface connected to the device, the rest of the network will trust that classification when the traffic passes through.