Interesting idea, I can't see why it wouldn't work. Most trap outs run for several weeks to reduce the colony size down so the queen is forced to leave with whatever bees are left.
With a trap out, all the field bees will be trapped out in the first day or two and cannot return to their home. From then on, in a normal trap out you will trap the bees out as they turn into field bees. With a lack of field bees, I'd imagine the house bees would turn into field bees earlier than they normally would. In your situation, by allowing access back to the hive, these 'new' field bees will be able to return so the colony can rebuild in strength.
I think it is very unlikely that the bees will abscond. If they did, another swarm would find it and move there one day anyway.
It won't matter at all that the entrance to your nuc is at the centre of the box. You can still put it as close as possible and it's not going to be very far away. They'll find it and the scent from the frame of eggs will attract them. I would put the frame of eggs in the centre of the box too. If you can, put the nuc box against the tree (so the bees can walk across the box and into the entrance), that might work better. I have noticed that bees walk around, looking for their old entrance, so if you can allow them to 'walk' to their new entrance, I reckon that would help.
All the best with it.