Over the past couple thousand hours I've had two engine outs. One shortly after rotation at 50 feet and 100 MPH. The other about a mile from the pattern just a bit above the pattern and accelerating.

The second one (in the Debonair) more approximates what you are talking about, other than with the wheels up it has almost twice the glide ratio of a 172. On closing the cowl flaps I immediately became aware of a strong oil smoke odor. I instinctively rolled into a tight turn back toward the airport. From slightly above the pattern altitude a mile out, I knew I could make any point on the airport. While in the turn I checked the gauges and saw the oil pressure was on the peg. I immediately pulled the engine to idle and hoped if I needed a shot of power it *might* still be there.
I was already at best glide and only slightly under pattern altitude so I chose to glide all the way around and land on the same runway from which I'd departed. I knew that should I find myself running out of altitude I could turn into the airport at any time. With a close in down wind and base being a close in U-turn from down wind to the runway I hit the gear down switch and pushed the flap switch to full as best glide is 120 and I normally land at 80 MPH minus 1 mph for each 100# under gross. Those big flaps and gear down add a lot of drag to the Deb. I still used a good half of the 3800 foot runway.

BTW you eventually learn the "feel" of the yoke and with an engine failure you just ease the yoke forward to maintain the same feel. So you sort of recognize and react as if you are on auto-pilot.

Regards and keep enjoying that primary training.

Roger