Does the relative abundance of radioactive isotopes reflect their half-lives?
Yes, the general idea you have is correct: isotopes with relatively short half-lives are found in quantities so minute as to be marginally detectable, and then only if they are being produced by something else: either as decay products of some long-lived isotope, or by cosmic-ray bombardment.
An example is gadolinium-150. This has a half-life of about 1.8 million years, and I believe simply does not occur naturally at all.  Gadolinium-152, with a half-life of about $10^{14}$ years, does occur naturally.
So whatever primordial gadolinium-150 there was has gone (in 4 billion years, you get a decrease of a factor of about $10^{669}$: the Earth contains around $10^{50}$ atoms, so there is a chance of $1/10^{619}$ of finding an atom of it on Earth).  Unfortunately in order to know how much there was you would need to understand nucleosynthesis in supernovae in considerable detail (gadolinium is heavier than iron and so originated mostly or entirely in supernovae), and I don't.  But I think it's safe to say that they probably made at least some, on the grounds that anything we do in the way of crashing particles into things to make isotopes (which we have done to make $^{150}\mathrm{Gd}$) supernovae also do, except much, much more.  If we assume the Earth was only a million years old, then about $68\%$ of the primordial $^{150}\mathrm{Gd}$ would still be here: we'd find it.
Now of course, there are two catches here:

perhaps the $^{150}\mathrm{Gd}$ has all gone somewhere secret where we can't find it;
this all rests on the idea of supernova nucleosynthesis.

So to answer the first: if this was true it would be utterly extraordinary.  In particular we spend a lot of time (really a lot of time) trying to isolate different isotopes of elements: people go to really enormous efforts to distinguish between different isotopes of uranium for instance.  This is something you can't do chemically, because the different isotopes have the same chemical properties.  Instead you have to do things like spin them in very high-speed centrifuges, or use mass spectrometers.  These things just don't exist naturally on Earth, so, since we do find other isotopes of gadolinium (including ${}{150}\mathrm{Gd}$, which is not stable), how come we don't find this one?  Well, we don't find it because it's not there, of course.
The second problem is perhaps more severe: people who believe the Earth is a million years old probably have no truck with supernovae at all, or are happy to just argue that, well, supernovae don't produce some isotopes because they just don't.  I don't think there's a useful argument against that.