I have one 4500 switch connected to the core with two fiber uplinks to two core switches (coreA and coreB). Both of them are in forwarding state because of the the per-vlan STP (depending on the VLAN). Recently, I cascaded one 3750 to the 4500 switch with just one straight-cable. Now, I need to connect the 3750 to both coreA and coreB. So at first, the root port of the 3750 is the FastE port. Since coreA and coreB are the root bridges, both of the fiber link will be the root port. Will it transition to root port and forwarding state immediately after I connect the fiber uplinks? I think I still have to wait for the forward delay timer for it to transition to forwarding state. Because I'm planning to disconnect the FastE trunk to the 4500. Will it cause downtime? Also, will it disrupt the 4500 STP state? By the way, I'm using rapid-pvst. Thanks.
The learning/listening stages are only used on ports that go forwarding using timers. With RSTP, things are different because of the proposal agreement mechanism. Basically, instead of waiting "some" time, the designated port on the core switch is proposing. As soon as it gets an agreement from the remote root port (confirming that everybody downstream is ok with the new root information), it can go forwarding, skipping the listening/learning stage. If for some reason the access switch was not answering the proposal (because it is running STP, or if the link was a shared segment for instance), then it would transition slowly to forwarding using timers.
As soon as you connect the 3750 to one of the core port, your 3750 will change its root port for all the vlans (assuming that the port channel between the cores has a lowest cost than the uplink between the 4500 and the core, which is likely). Switching the root port on the 3750 does not depend on any timer. I expect the convergence to be sub-second, but it's always better to do this after hours anyway. (exact sequence: (1) after receiving better info from the core, the 3750 blocks current root port leading to 4500 (2) 3750 puts the new root port in forwarding (3) 3750 sends an agreement to the core along with a TC indication (4) designated port on the port goes forwarding (5) core bridge propagates the TC.)
Then removing the 3750 uplink from the 4500 and connecting it to the other core switch will have the same impact (on half of the vlans only this time).