No...
If you are accessing two other computers, or the internet and another PC, then you might find it works out a little faster (will probably depend on drivers/OS). If your just surfing the web, you may find it a little (unnoticeably) slower, as the other NIC will be generating more traffic on your network (rarp etc.)
If you want a faster network connection (internally), make sure your NICs are gigabit, make sure you're using good cable that can handle gigabit (cat5e should do) and make sure the router/switch has gigabit ports (many routers that ISPs give are only 100mbit).