No, 32 bit/pixels is not related to whether the computer is 32-bit or 64-bit. You need to know your exact processor model. The very first Celeron D processors, from June 2004 (known as "Prescott") were 32-bit. The later generation of Celeron D processors (known as "Cedar Mill") were 64-bit.
Here I found an information how you can from under Windows XP determine if your processor is 32-bit or 64-bit. Note that this is different from whether you are running a 32-bit or 64-bit operating system. You can run a 32-bit OS even if your processor is 64-bit.
However, 1,5 GB seems to be very little to run Ubuntu with a full graphical desktop. Someone suggested Lubuntu in the comments - or, if you don't need a graphics environment (I don't think it's needed for a gateway), you can try a minimal installation of Ubuntu Server, which has no GUI.
You can also try a completely other distribution, not any Ubuntu variant, but that is off-topic for this board.