The legal aspect will depend on the wording of your MEL and when it applies and also if you are useing a Boeing QRH as they do clearly state that you are expected to consult the Dispatch Deviations Guide prior to take off and apply any restrictions. This is why the NNC makes no mention of the take off case.
It would also be a good idea to check your landing perf at destination and alternate and to consider the implications to your company and to consult them and when you've done all that better make sure you still have enough fuel.
Regardless of legalities commonsense, self preservation and a duty of care towards your passengers and crew should make you stop and consider the implications.
We all know (or ought to know) that there is a severe performance penalty for an inop anti skid so to launch on your interpretation of a legal technicality without due consideration to the performance considerations would demonstate a stunning ignorance at best.