[Arran]

In this case Mr Peteivan was speaking about an Atwater Kent radio and not a Philco. If this was 1952 or 62 I might agree, or even as late as 20 years ago you could take a chance. However if it's a choice between changing under $20 worth of capacitors with some hassle, or spending $100-150 on having a power transformer rewound if I couldn't find a used replacement I would prefer to change the capacitors. After all if the old caps die and take out a power transformer, a filter choke, or a field coil, you would still have to replace them anyhow. If you want to take the risk I would at least connect a pair of fuses in series with the high voltage winding, preferably fast blowing fuses, then when (not if) a cap does short out you will get a second chance.
Regards
Arran