Are floating point numbers denormalised before the processor performs arithmetic operations on them?
For multiplication, you simply multiply the mantissas and add the exponents, with a possible small adjustment to renormalize the result. There's no need to denormalize anything first.

For addition/subtraction, it is necessary to align the numbers, which means making their exponents equal before dealing with the mantissas. The number with the smaller exponent is denormalized in order to line things up. Obviously, if the difference in exponents is greater than the width of the mantissa, there's no point in completing the operation &mdash; the smaller number becomes effectively zero.

Don't confuse denormalization with the fact that the exponents are stored in "excess-128" notation. That's a completely separate issue. Yes, you need to convert that to 2's-complement before you do arithmetic on the exponents.