Reeve was pretty much a complete unknown to the general public (he'd done a soap opera role) and the only effect that had on the critics was to impress them.
What's the weekly viewership on True Blood
Which is not really relevant, anyway - unknown is probably best. If an actor's good, they're good.
I notice in an interview about Unstoppable
that Chris Pine is taking a very level-headed approach to his current celebrity - he's enjoying being able to pick and choose what he does, with the caveat that he doesn't expect it to necessarily last forever.