Hello guys,
Last week I had an usual scenario. We had no APU, and when we requested engine start at the gate ATC did not allow due to construction behind the aircraft. Our only option was to disconnect the EPU and to push back on battery only. Then they brought EPU and external high bleed pressure via vehicles. As I remember, when you are on battery only the mechanical horn will sound as the ADIRS are aligned. So before removing the EPU I turned off the ADIRS, then after push back completed and EPU connected I proceed with the alignment.
My question is: What are the consequences of leaving the ADIRS running on battery only? Are they going to overheat? That's what I was told and that's what I believe but I could not find any reference about it; It is just my assumption after checking the MEL about the mechanical horn. Some other guys mentioned it might drain the battery...

right?
Also I waited for ADIRS to be fully aligned before starting the engines... I never had this situation before and I was not 100% sure it would be a good idea since I had alignment fault just because of gusty wind or rough cargo loading in the past.
The FCOM just states that if alignment is still in progress while one engine is running it will be written in amber on the Ecam memo. I guess it might work just fine.