Yes, you are good to go. But make sure that trunks configured properly between switches. As VTP propagate it's information only over trunks.
This process might be easier if you configure all switches as VTP transparent. It's recommended to transparent mode. Because if somebody remove a VLAN by mistaken on VTP server it will remove that VLAN on all VTP client switches.
Anyway your configuration looks ok. There shouldn't be outage, because VLANs already exist on switches.
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After step 3, make one or more VLAN changes (on "sever") to increment the VLAN database revision number. (This to insure it's higher than a newly converted "client" in your existing step 4.
If you do step 4 next hop out, one at a time, from "server", you should see each switch pick up VLAN database with "servers" revision number.
I would also recommend you set a VTP (and same) VTP password on every switch. (Also insure VTP domain name is set too.)
You might also consider, if supported, whether you want to enable VTP auto pruning.
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