I don't often encounter this word like I used to, save the time of Lent or some other observed season. I hear instead words like "confess", "forgive" or "submit". Words like "Love God with all your heart & your neighbor as yourself" almost seem to surpass the necessity of conviction coupled with repentance anymore.
Can we confess our sins to God &/or one another with conviction but not repentance? Can we forgive others & neglect to repent of the same sins that find repose in us? Can we submit to one another out of reverence for Christ without a real change of heart? I think its entirely possible, yes. I've certainly done it. But God knows our hearts... our hearts, which will always betray us. The necessity of conviction and subsequent repentance are what make confession, forgiveness of another's sins against us, even the ability to submit to one another out of reverence for Christ not only possible, but effective & powerful.