Edge gluing tongue and groove (non locking) engineered hardwood to make floating floor over existing varnished chamfered-edge hardwood flooring

Yes, you can “edge glue the tongue and groove edge” provided: 1) tight fit between T&G edge, 2) temperature and humidity remains constant, 3) sub-base is stiff enough not to flex

1) The most important element is the “fit” between the tongue and groove. This “fit” must be tight...not snug, but tight. The way to check this is to pick up a board and hold it vertically. Then try to push another board into the groove. If it goes in easy, that is not acceptable. In fact, you’ll probably find that when it’s inserted all the way in, it will slide out (from just its own weight) and fall on the floor. (Don’t just check a few boards...check about 50%)

2) Fluctuations in temperature and humidity will cause the wood to grow and shrink. Obviously bad.

3) If the sub-base is not stiff enough the wood will “flex” and break the bond.

I wouldn’t. I’d install it as per the National Wood Flooring Association (NWFA) intended, by power nailing.

If you glue, you know you’ll still need to sand, right?

The original pergo flooring was tongue and groove you glued it and used special straps to pull it together to dry. So it can be done but a thicker tongue and groove may not hold up well because it is not as flexible as the pergo was. At a minimum I would build some straps using 1' cargo ratchet straps as the starting point then a couple of L brackets to hook on the edges to pull them tight together, this is how the original pergo system worked I think I had 4 straps that was enough for large rooms. I might try to assemble an area let it dry and try walking on it just to make sure it dosenot split.