Logic your thinking of NiCads.
Trust me NiMHs and Li_IONs if discarged too low can and will cause damage to the cells.
About storing batteries discharged, when you buy a car battery do they have to charge it up before they put it in? I've never ran into that, they store most batteries with a charge if they are intended to be used in the near future. Not discharged. I know an electrician, uses batteries all the time for critical radio equipment. He's told me before that they store their batteries with a charge becaue all batteries discharge themselves over time. If they get discharged to low the damage as Kurn posted can occur.