Can BuildCraft's Redstone Engines explode?

BuildCraft's Redstone Engines are slow, but I have always been taught that their one advantage is their inability to explode.

Is this true, or am I secretly in danger if I leave them on too long?

No, redstone engines don't explode in normal conditions (when are connected to something):

Redstone engines ... unlike Combustion engines, will never explode on running hot, except when not powering anything.

Unofficial Buildcraft Wiki

A single engine that is powering something cannot explode, period, even if the thing it is powering is doing nothing. However, it is technically possible to blow up a redstone engine if you have other engines pointing into it (daisy chaining power), even when it is powering something. You really do need to put effort into it to get it to explode.

Yes, any engine can explode if not powering something. However, only combustion (iron) engines will explode if not cooled. Cooling can be done with water (if it's a combustion engine) or turning it off for a bit.