Yes, he would have to start breathing again if he would be Moshiach.
But it’s not impossible, It can happen through techiyas hameisim. Hashem has done techiyas hameisim in the past to certain individuals. It doesn’t have to be through the big techiyas hameisim which will happen.
What my problem with some of the ideas floating around is the possiblity.
It is clear in the Gemara Sanhedrin 98b:
“אָמַר רַב אִי מִן חַיָּא הוּא כְּגוֹן רַבֵּנוּ הַקָּדוֹשׁ אִי מִן מַתְיָא הוּא כְּגוֹן דָּנִיאֵל אִישׁ חֲמוּדוֹת”
Btw, I want to pose a question to everybody: Why did Rav say if he is from the dead, it will be daniel, why daniel? If we want to say that we want somebody from the earlier generations, then why not say Moshe Rabbeinu? And if we want somebody from the latest generation, what happened to Rabbi Akiva, the Rashbi, and all the other huge talmidei chachamim and tzaddikim? R’ Shimon Bar Yochai sat in a cave for more than a decade and just sat and learned, why didn’t Rav refer to him as Moshiach Min Meisa?