Sure, that's ok.
Just a note about your title, "become + past participle"
It seems like you may be establishing a rule that would lead to poor and incorrect usage, like:
The apple has become eaten. (bad)
The paper has become edited. (worse)
The guests have become arrived. (awful)
This structure should more properly be entitled, "become + adjective"
Regarding the example you gave: Inhabited may be a past tense verb, a past participle, or an adjective.
Past tense verb: People inhabited the island in 2008.
Past participle: People have inhabited the island this week.
Adjective: I visited an inhabited island.
The reason why "inhabited" works in the example you provided is because it is an adjective.
The city has become inhabited.
Like: The city has become large.
Like: The city has become popular.
It is not true that you can use any participle with become. I hope this is clear.
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