Sure, or at least point you to the evidence.
The evidence is genetic. Changes in population size affect the frequency spectrum of genetic variation in that population in characteristic ways. Let's stick with variants that have only two alleles (e.g. single-nucleotide polymorphisms). If a population stays the same size for a long period of time, the distribution of allele frequencies is heavily weighted toward lower frequencies; specifically, the probability that a derived allele has frequency f is proportional to 1/f (or 1/(f(1-f)) if you don't know which is the derived and which is the ancestral allele).
A population that has expanded recently will have more low frequency variants than the constant-sized population, because the larger population can hold more variants, but the new variants haven't had time to drift to high frequency yet. (Note: "recently" here means any time in the last couple of hundred thousand years for humans.) A population that has been through a bottleneck, on the other hand, will show a deficit of low-frequency variants, since low frequency alleles often drift either to loss or to higher frequency during the bottleneck.
Non-African human populations show clear evidence for multiple bottlenecks. These include a bottleneck shared among all non-Africans, usually taken to reflect a small population migrating out of Africa, although there's nothing that says it couldn't include a contribution from Toba, since that's around the right time. It also includes additional modest bottlenecking in European population history, somewhat more in East Asia, and much more in native American populations.
African variation, on the other hand, shows modest evidence for a population expansion something more than 100,000 years, and no sign of a bottleneck around 70,000 years ago, or at any other time. For example, the first study to make a serious effort to fit human demographic models to variation data was published in 2005 (Genome Research 2005 Nov;15(11):1576-83.) It found bottlenecks in the history of European populations that amounted to an inbreeding coefficient of around 0.25, while for the African population studied the inbreeding coefficient was effectively zero (best estimate = 0.008). So the pattern really was inconsistent with there having been a population bottleneck in western Africa.
The next paper to do this kind of inference, by Alon Keinan and colleagues (Nat Genet. 2007 Oct;39(10):1251-5), found the same thing: clear evidence for expansion within the ancestral African population (by a factor of 1.8x, if I remember correctly), and no evidence for a bottleneck in the history of that population. Subsequent papers, using markedly better data sets as time has gone by, have been consistent in this regard. These include papers by Rasmus Nielsen, Carlos Bustamante and his group, and I think Gabor Marth. Probably others that I can't recall, too.
This is not to say that Toba could not have had any effect at all on the human population as a whole, but whatever effect it had was pretty small, and not a major determinant of our patterns of genetic variation.
