Is it possible to obtain gold through nuclear decay?
Natural gold exists, so the answer to the first part of your question is unambiguously "Yes". 'Cause all those heavy elements get made by transmutation in supernovae.
I can't answer the time scale thing because I haven't a table of the isotopes in front of me right now.
Checking with http://ie.lbl.gov/education/isotopes.htm I find that $^{197}$Pt has a beta decay branching fraction of about 3% and a halflife of about 95 minutes, and $^{197}$Ir decays by beta with 5 minute halflife and $^{197}$Os decays by beta with a 64 hour halflife...
Anyway, you can chase this as far as you care to.
I guess you are really looking for this wikipedia page : http://en.wikipedia.org/wiki/Synthesis_of_noble_metals#Gold .
In short, there are gold synthesis technique, but they apparently all need some external energy (either $\gamma$-ray or neutron capture) and are not restricted to nuclear decay. One of them has for intermediate step the nuclear decay${}^{197}Hg\rightarrow{}^{197}Au+e^+$ with a 2 days half life. The unstable ${}^{197}Hg$ is obtained from a stable $Hg$-isotope by $\gamma$-ray irradiation (${}^{198}Hg+\gamma\rightarrow {}^{197}Hg +n$.)
The following wikipedia link has a table of all the known isotopes of all the known elements. Gold has Z=79. According to the table, there's only one stable isotope of gold, $\;^{197}Au$ :
http://en.wikipedia.org/wiki/Table_of_nuclides_%28complete%29
From this you can figure out which isotopes decay into gold by considering the three possible decays (ignoring fission) beta decay, inverse beta decay, and alpha decay.
Beta decay means a neutron decays into a proton, an electron and an anti neutrino. The electron and anti neutrino go away. So the result is that the number of neutrons ("n" in the above table) decreases by one while the number of protons ("Z" in the above table) increases by one. The result is that you move in the table one square diagonally towards the top right.
Inverse beta decay is the opposite of beta decay (more or less). The result is that you move one square diagonally towards the bottom left.
Alpha decay means the loss of a helium nucleus of 2 protons and 2 neutrons. So you move two squares diagonally to the top left.
So if you want to look for chains that end with gold, do the following. Look at the isotopes 2 squares down and to the right (for alpha decay) or diagonally one square up right or down left (for beta decays). Now take a look at that isotope to see if it decays in the manner you've assumed. For example, $\;^{195}Hg$ is in a position to beta decay to gold.
To find out whether the isotope decays the way you've assumed, go to this website:
http://ie.lbl.gov/toi/perchart.htm
and click on the element, then the isotope. Clicking on Hg and then the isotope 195 shows that it does indeed decay to gold.
Note that this isotope can decay to gold in something like 46 ways. The different ways involve various excited nuclear states for either the mercury or the gold or both. Such excited states may also decay by emission of a photon (gamma ray).