Going from your sig, your ds is a month? I honestly think it is WAY too early for you to expect him to sleep through. He is still too little...

But to answer your title question, Spock is 19months and still doesn't sleep through.
I don't think the OP is expecting him to slee through, more so asking the question whether it is OK for him to do so if he is sleeping through... ie. should she wake him during the night if he is sleeping for long stretches.

I'm not sure on the answer to be honest, if he's four weeks, I'd be inclined not to let him go more than six or so hours between feeds.

I definitely didn't have this problem with either of mine, my "baby" will be 3 in a couple of months and he's never slept through