It won't be useless, but it will be so slow it will be painful. Also, many USB2 burners won't allow you to burn very fast when connected to an USB 1.1 port. I've seen ones go down as far as 4x for the max/cap for burning cd's...
If you want to put the burner onto a system with only USB1.1, look into adding USB2 via an expansion card. If it's a laptop, you can get USB2 PCMCIA cards. PCI cards will be very cheap, PCMCIA won't be as cheap. Either way, you shouldn't have trouble adding USB2 ports to any system (provided it has room for a card) for under $50 (for the laptop type).