No it does not. The "size" of ALU or number of bits is the size of tha DATA it can process. You can have a 2-bit ALU controlled by an 8-bit control word, thus giving you 256 possible operations with those 2bit operands.
Of course, two 2bit inputs and one 2bit output only give you at most 4*4*4=64 different combinations of inputs-to-output, but that is another story.
The same way, you could have a 16bit alu that only can do addition and subtraction, so it is controlled by a single bit.