Does saying "I was stolen by my sleep" make sense in English?

Yes, it can work. People can understand what you mean; however, because there is no similar idiom in English, it will sound unusual or perhaps even wrong to native speakers.

Something somewhere deep in my memory says to use robbed rather than stolen. But the metaphor would work for me.

Does saying “I was stolen by my sleep” make sense in English?

It can be understood by people who answer here on ELU. However that is because we are used to interpreting unusual sentences. The general population would probably not understand or they would just assume you were making a mistake.

There are reasons for this:

1. We don't usually talk about a person being stolen. That would imply they were property. In ancient Rome, I suppose one could steal someone's slave. A kidnapper might be said to steal a child from their bed - there is an implication in this that a child is the "property" of their parents.

2. Sleep is considered a state of consciousness. It is not considered capable of carrying out an action such as stealing. We would no more say "Sleep stole me" than "Sleep stole my wallet".

3. "My" is superfluous. We couldn't be stolen by someone else's sleep!

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As Stuart F says, "sleep stole over me" would be idiomatic in English".

In this sense "to steal" does not refer to robbery, it means as follows:

steal

to do something quickly or without being noticed:

She stole a glance at her watch.

He stole out of the room while no one was looking

https://dictionary.cambridge.org/dictionary/english/steal

As chanceoperation suggests, a somewhat similar idiom in (American) English is "robbed of sleep". Eg, "The noise in the apartment upstairs robbed me of my sleep last night."

This, however, appears to be almost exactly the opposite meaning of "stolen by my sleep" in the original question.

My take is that, given reasonable context, most English speakers would be able to figure out what "stolen by my sleep" means, in the manner that the original poster is using it.