32 bit PCI can handle 133MB/s I believe, in burst mode. (I could be wrong, this is off the top of my head) If it's right, that would be 1064 Mb/s (which is greater than 1 Gbps).
Do note that's a best case scenario. However, on a Gb network, you'd have faster switching, and less chance of packets colliding, especially if the machines on it are all limited the way this hypothetical one is. Additionally, I should mention that on a true network, you almost never hit anywhere near the stated "max" speeds. To do so requires specialized setups including specialized software. One way to hit almost a max is to have 2 computers linked in isolation with one being a UDP sink, and the other a UDP producer, then you might hit a sustained 100Mb/s in 1 direction. Any cross talk, or multiple computers, or too many switches/routers in the mix, and performance goes down. On any normal network of even 4 machines, max throughput is usually closer to 60Mb/s, and can drop significantly if multiple systems start moving data. I've seen fully switched (and badly designed) networks drop as low as 20-30% (and much worse in the days before fully switched networks).
So, long story short, even if you can't feed the data at 1Gb/s, you'd still benefit compared to 100Mbs as long as you can feed it faster than 100Mb/s.
Does that help?