How long will it take a whole beef tenderloin to reach 140?

140 is well-done for a beef tenderloin, that's bothering me a bit more than the safety aspects :). I'd take it to 130 the max! (obviously if well done is your preference-just don't think a meat like filet mignon is best suited for well done cooking!)
Restaurants use this technique all the time-however they hopefully have great habits regarding quick chill-down after searing, etc. A roast like this, uncut, really isn't a serious culprit for food safety issues. I understand the timing issues/guests/dinner party ideas, but it will only take you 10-15 minutes to sear this off well-and it seems like you have the time to bring it to room temp. So why don't you just sear and roast-it's the better root to take.
The timing will depend on your oven temperature, but this is not very thick and long-my experience is that 25-40 minutes or so in a 400 degree oven, but start checking the temperature at 15-20 minutes.

Seems like a weird way to cook. I've never seen anyone sear then refrigerate. If you can that crispy you can just broil it for a few minutes per side at the end. That should save you time and also since your meat will be cooked (and out resting at room temp) it'll serve to reheat and crisp it.

Was it a specific recipe that advised searing then refrigerating and bringing back to room temp...? Because, to me, that method seems risky from a food safety POV for the same reason you shouldn't refreeze something you've already defrosted: too much opportunity for bacteria to thrive. There are a lot of food safety experts on here who post regularly, though, so hopefully they'll chime in and correct me if I'm wrong.