It works. It's something that isn't really used that often, but I am absolutely unable to explain why, especially as it's frankly a more logical construction.
I think it's kinda like "No, you assumed wrong, we are not at home" while "nie ma nas..." just expresses that we are 'absent' from home...
It may be easier, but it's not what people usually say ;)
I went through the national corpus: http://www.nkjp.pl/poliqarp/nkjp300/query/
"nie ma X w domu" has 117 results with personal pronouns (search for: nie ma [pos=ppron12 | pos=ppron3] w domu)
"nie jestem/jesteś/etc. w domu" has 7 results (search for: nie [orth=jestem|orth=jesteś|orth=jest|orth=jesteśmy|orth=jesteście|orth=są] w domu)
In Past Tense and Future Tense we use "być" (nie było mnie w domu/nie będzie jej w domu), that's why the second query needs to use all the Present Tense forms listed separately, so other forms of "być" aren't put there. Also, we do accept "nie jesteśmy w domu" since recently.
So is this "lets say" as in "Let both of us say the words that we are not home" or as in the only other way it could be interpreted as? I actually dont know how to explain the second way it could be interpreted, maybe metaphorically? Like "Lets say we werent home, what would you do?" Anyway, my question is which way can this be sentence be interpreted as.
The Polish sentence has the same two meanings that I can see in English:
We should say the words "We are not home".
Supposedly/Hypothetically, if we're not at home, what happens then? (The mailman is supposed to bring an important package, what if we won't be at home when he arrives?)