I am not an expert but I'd say probably not. If something is going to explode, it'll probably do so when power is applied and not after. Having said that, arcing wires, lithium-ion batteries and some appliances like heaters can create a fire hazard. Also, I don't know about the PS2 but like you said some devices go into sleep or hibernation after a while which would only draw very little power. Even if the PS2 didn't have that feature, it's probably not drawing that much power. So basically, anything that has power could pose a risk but it's probably fine if it doesn't immediately die when turned on.
I wouldn't worry about it.