"My gut feeling is to to translate this as "because of that, can (I) really take a breather?"
Mine is to translate it as "Let's take a break then, shall we?"
I used the all-purpose "then". I could not think of a situation or context where 「それなら」 in 「それなら一息入れようか」 would mean "because of that", but you are the one who knows the context.
" (very strongly implying that I can't) or "I can't really take a break"- would that be correct?"
No, it would not. Wonder what words lead you to think that way.
Under normal circumstances, 「それなら一息入れようか。」 would be said only when the speaker thinks it appropriate to take a break. Though there is the question particle 「か」 in there, all it is saying is really just "Let's take a break!" If the larger context proves otherwise, you should provide it.
"Does it feel similar to: 「 それなら一息入れるまい。」?"
No, not at all, I am afraid. Why bring in a negation auxiliary verb here?
I feel it would be either:
1) 「それなら一息入れようか。」 was said in an extremely unusual situation that is beyond the imagination of an average J-speaker as myself. Or,
2) You are somehow seeing something that is not in the sentence. (Perhaps because you are reading too much into it?)