Is Kabbala proof that Chazal could not make mistakes in science?

IMHO the answer is no.

R' Feldman writes
One of the most powerful reasons why R. Avraham’s opinion was rejected by most opinions, is the introduction of the wisdom of Kabbalah of the Ari Zal in the sixteenth century. This cast the Sages in another dimension.

While this statement is very debatable, I would like to approach this from a different angle.

The Ramban who was one of the greatest Rishonim, was also according to everyone, a great mekubal. And yet, the Ramban, in at least 1 place in his commentary on Chumash implies quite clearly that Chazal could make mistakes in science.

The Ramban at the beginning of Parshas Tazria quotes Chazal as follows
איש מזריע בו לובן שממנו גידים ועצמות ... אשא מזרעת אודם שממנו עור בשר ודם
The man provides the white from which the bones and sinews grow ... the women provides the red from which the skin, meat, and blood come

This is clearly a scientific opinion of Chazal. The Ramban then quotes the Greek philosophers who disagree with Chazal
ועל דעת חכמי הפלוספי היונים כל גוף העובר מדם האשה אין בו לאיש אלא ... שהוא נותן צורה
And the Greek philosphers say that the all of the body of the child comes from the blood of the women the only thing that comes from the man is the tzura (whatever that means)

The Ramban clearly and unequivocally records the opinion of the Greek philosophers who argue on a scientific fact of Chazal even though the Ramban was one of the greatest mekubalim. We see clearly that kabbala did not teach Chazal science and that the Ramban (who was not from the rationalist/philosophical rishonim) also holds that Chazal could make mistakes in science.

Update

Here is another Ramban where he writes explicitly that he accepts the opinions of the Greek scientists and bases pshat in a pasuk on that.

Ramban Bereishis 9:12
"This is the sign of the covenant that I give" - It would seem from this sign that the rainbow which appears in the clouds is not part of the acts of creation, and only now did God create something new, to make a rainbow appear in the sky on a cloudy day… But we are compelled to believe the words of the Greeks, that the rainbow is a result of the sun's rays passing through moist air, for in any container of water that is placed before the sun, there can be seen something that resembles a rainbow. And when we look again at the wording of the verse, we will understand it thus. For it says, "I have set my rainbow in the cloud," and it did not say "I am setting it in the cloud," (in the present tense) as it said, "this is the sign of the covenant that I am giving." And the word "My rainbow" indicates the rainbow previously existed.

The Ramban writes that we are compelled to believe the Greeks that a rainbow is a natural phenomenon that has existed since the beginning of creation even though it contradicts the simple pshat in the pasuk.