You can connect your servers anywhere in the network. In a typical two or three tier network, servers would be connected to Top of Rack access switches. Or at a push the distribution switches if the access layer does not provide the required port speeds.
Connecting your servers to the core may seem appealing if he server is providing a critical service, but switchports on a core switch linecard are expensive and should be used sparingly. Also in a 3 tier design the routing for user/ server VLANs would be carried out on the distribution/ aggregation layer, so a core switch connection would be the wrong position.
As a designer I have a few points:
1. Core switch ports are very expensive compair to top of rack switch ports.
2. Server ports are required configuration changes many times and it is not advisable to do this think on the core switch.
3. 3Tier network, we will perform intervlan routing at the distribution layer so there will be an extra delay & extra load on the links for accessing the server resources by the client.
4. As core switching is basically for the routing but we need many Layer 2 connectivity for servers as HA heartbeat, migration link, etc.