If we follow the storyline, I would say this is not logically and also it is impossible to achieve it.
Here is the reason why it is impossible to perform it.
Perform Shadow Clone Jutsu and Tsukuyomi will cost a lot chakra and also have it's side effect.
Using Genjutsu especially Tsukuyomi, is really consume a lot chakra and also hurt your body as well. (Itachi is a great example. Plus not every Uchiha know how to use Tsukuyomi.)
Using Shadow Clones Jutsu also need to consume a lot chakra. Tobirama Senju also mention that if you over used this jutsu it will cost your life eventually. (Naruto can use his shadow clone because inside his body have Kurama (Nine Tail Beast).)
Let's say in a day, you only can use 5
- Tsukuyomi cost 2
- Shadow Clone cost 2
That's right, if you use both of these skill, you only have 1
"Mana" left (
5 - 4 = 1)and that will cost your body exhausted or even you may collapsed. (*Another Kakashi? joke aside.)
Shadow Clone is kinda weak.
Let's say you successfully cast Tsukuyomi on your clone and go through your 10 months training. We know that Shadow Clone is very weak, even a little bit scratch could make your clone disappear. Who can guarantee that during those 10 months training your clone will not hurt?
Worst thing come, your shadow clone accidentally hurt himself during the training and it disappear. *Pop....You wasted your chakra and maybe laying on the bed after that.
Genjutsu wouldn't make your body gain muscle or increase stamina, it just affect your mind only.
Let's say you successfully cast Tsukuyomi on the shadow clone, your shadow clone successfully go through the whole 10 months training and the shadow clone seems like a bit muscular.
But in reality, the shadow clone only pass 10 sec. Even if you "close" your shadow clone jutsu, there is no evidence say that the muscle will instant transfer back to the real owner body. Even if you cast Tsukuyomi on to yourself, the result I would say still the same.
(I don't know how to describe when you wanna turn off your shadow clone jutsu so I use close.)
The only thing that transfer to the owner is the mind of the shadow clone. Maybe you will remember what your shadow clone did during those 10 month.
EXAMPLE: Remember back the day Naruto practice his Rasen-Shuriken and Sage Mode? Naruto use his shadow clone because he want to quickly memories how to control the flow of the chakra and by using his shadow clone, there is a possibility that one of the shadow clone successfully did it correctly and when it disappear and return to Naruto mind, Naruto will be like oh, "So this is the way that shadow clone did it huh."
So what I want to say that using Shadow Clone practice the physically workout won't make your body strong(or should say upgrade?). It only the mind that affect. (If I have this skill I can read more book. heheh)
You may say why some people collapse after they got hit by the Genjutsu. Isn't this affect your physical body as well? No.
As you can see:
"A Genjutsu is created when a ninja controls the chakra flow of a target's cerebral nervous system, thereby affecting their five senses; this is frequently used to create false images and/or trick the body into believing its has experienced physical pain". (False, trick, believing its has experienced. It's like my mind thinking about eating 2 set of McDonald but in real life, I'm still hungry.)
Conclusion, even you successfully cast Tsukuyomi on to the Shadow Clone and the Shadow Clone also successfully pass the 10 months training and when you "close" the Shadow Clone, what you will gain is only you know what have he done the those 10 month.
Yes maybe you discover some insane movement but your current body is not capable to do those move yet because your body is not reach that level. You can imagine yourself like you have a time machine and went back 10 or 20 years and you found that you're still a little, short, small kid but your mind is like full of knowledge.
If you say not follow the storyline, (For example Itachi didn't become the criminal and help Naruto in his training. Maybe it will help him grow more faster and stronger. But as I mention above, using Tsukuyomi is cost a lot chakra and hurt your body as well. So for Itachi this smart person, I would say that he will not using this method to train someone. *If the plot wanted then I have no words to say so. ) it MAYBE work. But technically this situation wouldn't happen.