Does full nose up trim provide approximately the elevator pressure for Vg?
This technique is commonly called the "minimum trim glide" - basically you smoothly trim the aircraft to full nose-up after the engine quits (at a rate which won't cause it to "balloon"), or alternatively you establish best glide speed manually and then trim to full nose-up to relive the pressure on the yoke so you can concentrate on other things.

I'm not sure if this is a "certification requirement" (I can't find anything about it in Part 23's discussion of trim requirements, the old CAR 3 regulations, or in AC 23-8C.

Empirically I can tell you that it's true for the loading configurations I've tried it in, on the Piper PA-28 and Cessna 172 aircraft I've flown. I have been lead to believe it is generally true for single-engine piston light aircraft: With no engine thrust full nose-up trim will produce something close to best glide speed. Before relying on it in any particular type of aircraft however I would perform a test at altitude by bringing the power to idle and verifying that you get something reasonably close to best glide speed.



Note that there is a potential pitfall of the minimum trim glide when practicing engine out maneuvers: Upon recovery it is possible to cause a trim stall. As power and airspeed increases in the recovery elevator/trim authority is also increased, and full nose-up trim is generally adequate to cause the aircraft to stall in this situation, therefore special care must be taken to prevent the aircraft from pitching up to an attitude which would cause a stall.