Are you talking about "aggregating" your bandwidth? The answer is a (very) qualified "yes," but it has a very large "but" attached.
That "but" is simply "it works ONLY if you have a big enough pipe to provide the data, AND if your computer(s) can handle the bandwidth you're looking for. A gigabit ethernet card will saturate the PCI bus if it really gets a gigabit connection. On the other hand, having two or more 100BaseT cards probably won't saturate the bus, but you'll need special drivers to combine the signals-and here's the real pain in the "but": you need special connection equipment to take the big data pipe's data and split it up for the multiple cards.
So in theory what you're talking about is feasible and even workable. In practice, for a home or small office user, it just isn't workable.