I just tried this out on a 6224 and this was my result:Made telnet connection, ran copy command, received same prompt as you, continued, went a few seconds without being able to enter any commands, then the switch went back to a console prompt. It did not kill the session for me, I just could not input anything while the config was being saved.  However I imagine that if the switch is being heavily used, and you have a lot of changes that are being saved, that it could take a little longer. The 2-3 minutes is going to be a worst case scenario.  You can use these commands to check the CPU/memory before saving.  • console#show process cpu  • console#show memory cpu Hope this helps. 
I've done this billions of times on Cisco switches, and "copy run start" takes seconds.  When I tried it on my 6248 switch, I get, "This operation may take a few minutes.  Management interfaces will not be available during this time.  Do you want to save  (y/n)  I'm connected to  the switch via SSH -- if I follow through with this config, will it really kill my SSH session, and lock me out of SSH for 2-3 minutes??.    I have 5 VLANs active in the config, and about 20 of the 48 ports are active.  I have a single   4-port  LAG  interface to another switch.   No spanning-tree is configured or needed; everything is in portfast mode.  Thanks!
'Copy running-configuration startup-configuration' takes minutes??