"Sealing in the juices" is definitely false, but a hot sear to cause the Maillaird protein reaction is important if you want to have the distinctive "traditional" steak taste.
Definitely after. Cooking denatures the myosin and releases water; a seared steak soaking in water isn't going to have the kind of texture you'll get (and want!) from the Maillard reaction.
I guess what I mean is that it'll taste fine but the texture won't be quite there.
That's good for a 1-hour steak, but I wouldn't do eggs this way (needs more precise temp) or a 72-hour short rib braise (needs stable heat for longer).
I agree--and even for one hour timeframes, be sure to check your ending temperature to make sure it didn't cool off too much. I'm not a fan of the beer-cooler method for this reason (although with care, of course, it's safe).