Can a power conditioner blow a fuse?

I don't think you have a power conditioner either. I suspect you simply have an extension lead, probably with a surge protector on it. That latter is there to protect from, for example, lightning strikes causing a surge in the power.

You cannot safely add devices ad infinitum without risking an overload. I hope the outlet is fused, or you could be in for a fire. You need to calculate what your outlet can take. For example, here a 13 amp socket at a conservative 220 volts can handle up to 2.86 kilowatt. That's the maximum I'd load it with, in fact I go considerably lower for safety's sake and to avoid hot cables and fittings etc.

not true. the 'power conditioner' will turn itself off if you overload it

What you describe IS NOT a power conditioner. It is ONLY a multi-outlet extension cord.

By itself, it wouldn't blow a fuse unless it is defective.

However, by allowing you to connect more items to one circuit, it makes it easier to overload the circuit.

You better hope that outlet is fused somewhere. The power conditioner merely guards against lightning hits to some extent. However much all those items draw is all running through that one outlet and the power conditioner. If you can't figure it out then you need to call an electrician before you wind up burning the house down.

not true

as you plug in more units , the current load increases until the unit fuses or the wires catch alight and burn the place down

Whoever told you that was wrong. They were guessing that a good power strip will have a breaker on it that will trip before the panel's circuit interrupter, but either your conditioner isn't so equipped, its breaker failed to open, or your panel's circuit breaker or fuse is old and getting soft, easier to trip.