That´s a pity...
Well, the rifle is gonna have 3,5" shorter tube, if can be done. Cut it at the nick, rebreech. The wall thickness is on the pretty low "just enought" side even without the nick. No matter what the steel is, the nick makes inconsistency in tension distribution. For sure the material will have tendency to elongate on the lower part of the barrel, creating stress in the upper portion. Hard to say if after several, or after several dozen shots.
Yes, the barrel is a wristbreaker, if one counts near- or full-amputation as a "break". Played with several mild steels and wall thicknesses some years ago, trying to figure which can be used for a barrel and what the most dangerous machining marks, flaws and oops are those which makes man sniffing flowers from the less colorful side. And such a nick is gonna make someone ugly problem.
Looking for paralell with a dovetail is false, because no sane person would put a dovetail on such a thin-walled barrel less than foot from the breech (I hope).
Edit
in reaction to snyder:
We know nothing about the material specs and grade used on that barrel. So such a paralell is absolutely OFF!!! AND one of most dangerous statements, which can be said.
To hold securely and repetitively pressures of BP, you need 4,5-5 mm (1/6"-1/5") of about 1018 steel-wihout the tread. But the same you can hold easily by only 1/25" of properly heat-treated 4130 or 4140 alloyed steel. The ultimate tensile strenght is not what counts here-it´s the safety margin to actual yield strenght, what makes the barrel safe or unsafe through more than one or very few shots.