Yes, it will run teh charger and as long as you're not charging over 7, maybe 7.5amps, it will work. You won't be able to use some of the other features like motor breakin or powering a lathe though. I believe the charger needs 12amps to for those features.

I ran mine with a 12a supply while DTX recommends a 15a continuous supply to make the Ice fully functional. ProPeak makes a 20a supply which is one of the supplies I'm using now. It would be money well spent if you could swing the bigger supply. This would make the supply viable for your next charger when that time comes.