Is a sentence's deep structure representative of i-language?

The distinction to keep in mind is competence and performance. Chomsky is exclusively concerned with competence, ie. the knowledge of the language system. Deep structure is what defines the competence but it is not active in the process of performance (except in some very constrained contexts such as garden path sentences. Nobody assumes that we're actually generating sentences from some deep structures during the process of utterance. However, the deep structure places constraints on what can be said and what is said.

Of course, Chomsky (and most generative linguists) don't actually use the concept of deep structure any more. The earlier concepts of deep structure have moved to the notion of Universal Grammar. There are some theories like the Prague Functional Generative Description framework that postulate something akin to deep structure (they the FGD people call it tectogrammatic level) but they still would not claim this to be a part of performance.

However, your summary and the actual question are contradictory. I-Language is NOT "what's happening in our head when we speak" that's a description of performance while i-language (for Chomsky, if I understand him correctly) is still a part of competence. It's just a different way of looking at what competence is. It is contrasted with e-language to cover all the externalities like communicative and social knowledge.

Finally, it's precisely this sort of question that has led many linguists (myself included) to abandon the performance/competence distinction and postulate the usage-based model of language.