What I do
is I do several quotes with different options. I usually insure the bike without security. So for example when I was keeping it on a drive, it was insured to be kept unsecured on the drive. This is because the risk of me crashing was seen as higher than the risk of theft and so the cost was the same. It also meant that if on one occasion I forgot to secure it, they couldn't screw me over. If you insure it with locks and chains it is assumed you will be using them all the time and if you don't you may not be insured.
So if it's insured as "left overnight on a private drive" with no security devices attached to your policy, my understanding is that this means it's insured if you leave it not locked up on the drive. Obviously you'd be mad to not secure it properly with a good chain and lock - a proper one, not a £20 job that a junior hacksaw will see to. If you want to reliably find your bike where you left it, then you want to be spending £100+ on a chain. I use a very high quality alarmed disc lock when I'm out as I park in very public places. If I was parking in quieter places, I'd be securing with my exceedingly beasty chain.
So in conclusion - it depends on how you insured it to be left overnight and what security devices you specified on the policy. If you specified security, it must be employed and if it gets nicked you may well be asked to provide evidence of damaged chains / locks. If of course you fake that and the police find out, you'll be charged with perverting the course of justice as well as any fraud offences you've committed - the former alone often carries a custodial sentence as they don't take it lightly.