Online, you can find this example of 同学 being used as a separable verb:
我和他同过三年学。
He and I were classmates for three years.
I'm skeptical this is correct. (Sometimes databases have errors, and those errors are copied into other databases.) Or, if it is correct, I feel like it's a very uncommon usage.
Question: Can 同学 really be used as a separable verb?
To say "no" is rather prescriptive. The phrase "同过 X 年学" or simply "同过学" is not so uncommon in real life.
Pro-tip for advanced learners of Chinese: nouns can sometimes be used as the predicate directly, without a linking verb. Some scholars even argue that the separation of verbs and nouns in Chinese is artificial and they are actually of the same part of speech (eg. 沈家煊《名词和动词》).
同学 is strictly a noun, 我和他同过三年学 is ungrammatical
The classical version of 同学 is 同窗
同窗 is mainly a noun, but it can be used as a verb in classical style speech
Example:
你我同窗三載 - you and I studied together (in the same school) for three years
他是我同窗好友 - he is my classmate and good friend
同窗 as a verb is not separable, 我和他同过三年窗 is also ungrammatical
I consider the speaking is correct, as 同学 is composed of two words "同" and "学", put the words together, it becomes a noun - "schoolmate", but the words can be used separately and interpreted as "learning/study(学) together/with(同)", and implies "a shared(同) experience or place(学校)".
我和他同过三年学。- "He and I were classmates for three years." implies the shared experience in the same place - He and I have/had been learning/studying together/in the same school for three years.
A similar expression is "我和他同过三年房/宿舍" - He and I (we) have shared a room (under the same roof) for three years. The equivalent is "我們做過三年的室友". And "我和她同过三年床" - "We have slept together for three years", or, depending on the context of the question that draws the answer, "We were spouses for three years".
The answer is no.
Splitting 同 and 学 is usually seen in southern dialects, and is by no means the standard usage. It does not make sense both in modern context and archaic language.
You can use 我和他做过三年同学，and 我和他同学过三年 is acceptable as 同 and 学 are interpreted as two separate words.
