The GMAT does not test whether you're a 'human calculator'. While you do need to be completely comfortable multiplying small numbers -- you shouldn't need to think about what 8x7 or 11x12 is equal to -- you won't need to multiply two awkward large numbers, or square any awkward large number. On some questions, it may, at first, appear that you need to do a strenuous calculation, but there will almost always be a way to avoid it. For example, you might be asked to find:

3201^2 - 3199^2

Of course, we could square 3201, square 3199, then subtract, but that could be a lot of work. Instead we can notice that this is a difference of squares:

3201^2 - 3199^2 = (3201 + 3199)(3201 - 3199) = 6400*2 = 12800

If you have a lot of time to study, there's no harm in learning the sorts of tricks you mention, but there are certainly more important things to know.