First yes only machine is talking at a time, but that's not a concern at these rates.
Second, can your cable plant handle Gig traffic? If not the card will (defaultly installed) auto-negotiate the next fastest connection, say 100 MB. I assume you already have that in current hardware. Below will discuss optimizing your netowrk and/or replacing components.
How many users do you have? Keep it simple, there may be no need to upgrade. These are the questions that you have to answer before you can even guess at your network's performance.
Are all of the clients on a hub or dedicated to a switch port? If they are dedicated to a switchport, then cut the client network cards to auto-negotiate and throttle the switch ports back half duplex. This will force each client workstation to 10MB. then put the server in the switch dedicated at 100 MB. This will keep any one machine from momopolizing the Server's resources. All users will see an improvement, unless you have 150 and one server.
If you can take the server and get it out of the broadcast domain with the clients, use helper-addresses on a router if it's also a dhcp server. This will reduce the amount of broadcast traffic the server has to process. (Not sure that an application server makes a good DHCP server, but hey you know your budget and your network size.
Take metrics of your current bandwidth utilization before you implement anything. This will help with determining if you have actually increased productivity.
Bottom Line, give the users 10 MB a piece, and the server 100 MB will allow 10 concurrent non-stop connections at a full 10MB before the server is at 100% cap.
NOTE: If you can support GB ethernet and you have the money, upgrade the server, then move the client's switch ports to 100 MB full, an the server at GB full, this will allow for the same scenario, but 10 times the bandwidth. I have to say that your network must be GB compatable before you move the server there. If you upgrade the card now, but the switches only support 100 MB,...........well, your server will be ready to go when you upgrade your switch.....
I can also tell you that if you use the 6509, experience with auto-negotiating Gig cards causes link flapping and intermittence. While upgrading the server's max throughput, you may hinder connectivity.
This will take some testing of the idea product...
Good Luck.