Is it possible to migrate on new hardware with just IP switc

[MrSax]

My old server is overload and I want to migrate to new one with as less downtime as possible. Idea is to install debian (jessie) on new hardware and make identical configuration like old one except IP address. (so - same hostname).
Then I copy all files (users, mails, folders.. databases, web...) And then just swich IPs on old and new server.
My question is: should I expect any problems (dhcp, bind, postfix, apache...) at time when both server are up?