If you watch the IRS when you switch them off, you will stay that they stay powered for about 30secs. The computors are collecting information. Then they turn themselves off. They are now dead and can be switched on again.
Some computors do need longer before switching on again. The FMGCS is one. It has capacitors inside it to allow for power transfer and will retain information for ages. The MM says 7 mins before it has reset.
But the IRS relies on the batteries and as soon as the lights are out you can turn it on again.
The reason for doing this before a long flight is that on the older IRS there was alimited memory (the old BA A320 have this type) and you could run out of waypoints!! Bit embarrassing if you are in the middle of nowhere! But new IRS should last a lot longer and a Quick Align is enough during the day.