With some electrical items (especially those with metal casings), such a plug is fitted onto the end of a three core cable, with the 'earth' lead connected to the metal case or chassis of the appliance. Dispensing with the earth connection would remove an essential safety back-up when using the appliance. (However it wouldn't stop the appliance from working normally. The earth connection does nothing until a fault occurs).
With other electrical items there's only a two-core cable feeding into the plug, with the earth pin left unconnected. So it would make no difference at all if you simply dispensed with the earth pin.
So, without knowing whether it's a 2-core lead, or a 3-core one, it's impossible to answer your question accurately. (However I'd guess that a laptop's power adapter might only have a two-core cable).
I'm also confused as to how you could have an extension lead without an earth connection anyway. This website is based in the UK, where we've got a 230V supply and any extension lead would always have a 3-pin socket on the end of it.