It does not have a big time save on easy. It just makes the fights faster if you are over trained but the training causes a time loss. On normal or hard it offers completly new strats because you are able to use this glitch to train a specific stat to the next decay threshold. It also makes it possible to play the fame fights as on easy if you can train without stat decay.
I tried the glitch on the initial push ups in hopes that maybe you can level enough to beat the first fight, just to see what would happen. Sadly the push up mat runs out of juice around level 3 in str, agi, and stm.
HOLY CRAP, menu glitch makes time pass extremely fast when working on the construction site! This will be great when you just need advance time.
Forgot to mention that it works for sleeping as well. Unfortunately, the menu glitch is not really precise so over sleeping or over working is possible which could destroy my whole routing. If you click on menu when the day changes so that the result screen disappears, it does sometimes not allow you to fight. It happened to me that I worked on day 11 until day 12 with the glitch but I was only able to do the league fight and not the ultimate fight until day 13.
Menu glitch does also work with Party and Advertisment in Ding Kong section. But as in Russia you will not receive any food production. I would recomend to do this only after the trailer park glitch with 18 energy drinks. You don't get softlocked as in Russia but buying always 7 food and and 7 energy from Apu costs a lot of money.