No. You pay casting cost for Steal Enchantment and additional cost for attaching it to new target, not cast and reveal stolen enchantment. Enchanter's ring can be used when You're casting an enchantment only and with Steal Enchantment You're just paying additional cost for attaching to new target. "As if You just cast and reveal the spell" refers to the cost calculation.
Also important is "just cast" in SE vs "You are casting" in ER. You don't have a time window to use Enchanter's Ring. If You were casting the stolen enchantment Nullify, Harshforge and other things could be applied to this, but they aren't.
[mwcard=MW1Q09]Enchanter's Ring[/mwcard]
[mwcard=MW1I27]Steal Enchantment[/mwcard]