Theoretically, a one gig port being hit by mutiple gig ports at the same time will be over-subscribed.
In reality though, your backup server generally wouldn't aggregate traffic along with your other servers, since most backups happen after hours, when your other servers are not busy. Your Email server works sporadically, as with your print-server as well.
The fact that you question this issue or possible issue Brings up a question on my part, are you experiencing problems with bandwidth? My guess would be that you're not, but if so there are things you can do to mitigate bandwidth saturation, before spending money on 10 gig. ports, modules, and switches. Your backup server can be put on it's own separate VLAN, and any servers that are to be backed up given a nic with the appropriate backup VLAN ip address. You can also aggregate links, or in Cisco nomenclature, EtherChannel links. Don't quote me on the no. of ports but I believe up to 8 ports can be channeled.
This would give you 4 gig. links (current bandwidth x 4) plus give you redundancy in addition. In regards to channeling, the biggest issues is, can you spare the ports?
I hope this helps.