Often times people asking here expect night and day differences between audio electronics, just to be met with the realization, that the transducers are the most noticable part of the chain.
That being said, the NFB-11 hasn't been measured here, but since it has "No FeedBack" (at least I assume that's what "NFB" means) in the name, I'd assume is performs just like all the other Audio-gd products. Of course you can't trust the manufacturers specs since they are known to just make things up, and the build quality has been shown to be questionable to dangerous.
If it gives you a SINAD in the mid 50's like some of their products, there would be an audible difference to something >96dB even if the output impedance is low and output power is sufficient.
As far as power goes, the manufacturer specifies 300mW/300R, so if it, in a manner similar to the R2R11 tested here, reaches half that in reality, it would be sufficient. Output impedance is specified at 2R, wich is probably more or less correct, safe to say it's fairly low, doesn't matter too much with the HD800.
As you might be able to tell, I don't like Audio-gd very much, in fact I think it's one of those scummy companies that gives Chinese products a bad name.
Anyway, upgrading the DAC/Amp will probably make a very noticable difference in this case.
A Shiit Modius/Magnius stack is a pretty good option at 400$ for the both. If possible, you should use a balanced cable then.
If you don't want balanced but save some money, you could of course buy a JDS Labs Atom stack, a Schiit Magni Heresy and Modi 3+ or something that is not a stack at all and just mix it up like you want, I use an Atom amp and a Topping E30 for example. Have a look at the feature lists and decide what you need. You could of course also buy a good interface (Motu M4 for example) and combine that with an amp for desktop use. If you want something attractive, the JDS Labs Element II would fit that bill at a budget.
There are many good options at reasonable prices these days. Here is a link to the ASR measurement index for an overview (some of the lastest revies aren't listed there yet):
Audio Electronics Review and Measurements Index | Audio Science Review (ASR) Forum