When the engine quits you become ballistic (in more ways than one). I use my gear like speed brakes, when close to 120 I drop 'em and instantly I am at 120 and dropping.
Why you would lower your gear after an engine quit is beyond me unless the GUMPS sequence is so thoroughly into your mind you can't help it (engine failure is an immediate indicator that some sort of landing is imminent).
When close to the ground; i.e., shortly after TO, so many factors come into play that are working against you that I don't think you can speculate at what altitude you might be able to get the turn in. Presumably, since you are in TO phase, you have a headwind. That's helping with lift, but without an engine it's also trying to slow you to a stall. Once the turn commences it becomes a crosswind and then a tail wind. If you are basically doing the kamikaze to get back on the ground, two things are certain. You will maintain useful airspeed and you will get to the ground very quickly. At issue is where.
One thing I will point out with my E is that the engine is often off (well, idle) when I land a squeaker. Mooneys like to float and I'd be happy to take a wham, bam, thank you ma'am bouncy landing if the engine quit. Of course, with the gear up there would not be a lot of bounce