Hi Pineteam, If you left the IRS 1 on all night - then it might drain the battery flat.
This iinfo is from my original paper Training manual in 2003 from Airbus.
ADIRU 1 power supply is normally AC ESS but will take power from HOT bus 2 until the battery is flat.
ADIRU 2 will take power from HOT bus 2 for 5 mins.
ADIRU 3 will take power from HOT bus 1 for 5 mins.
so I guess you could have left the IRS in NAV during push back provided you were re-connected with power within 5 mins - else IRS 2 and 3 would have shut down automatically.
I can send you pdfs of the relevant pages.
Nav Electrical power supply
Electrical distribution