If it's headed for a German port yes. If it's bound for a Dutch or Danish one that's another matter. Americans weren't happy about Britain blockading neutral ports, particularly since their definition of contraband was constantly expanding. Sinking a vessel bound for Amsterdam would absolutely create a diplomatic incident, but it would be more likely to lead to cutting off support, not a declaration of war.Sailing willingly into a active warzone, subsequently refusing to stop when questioned and then trying to outrun RN ships isnt really a diplomatic incident, its a person being an idiot. The Royal Navy didn't tend to blow ships up but if they for some reason had to instead of just buying the cargo, the US would probably write that captain off as a belligerent unfortunate. Shit happens in war, hardly grounds for ending support to the Entente.
Absolutely.Itd have to be a big passenger liner that maybe ends up at the wrong place at the wrong time, is misidentified as a German warship and is sunk. Even then the British would like apologize, offer compensation and maybe try the captain involved to appease the US. The US didn't need war to apply pressure either, they could do it financially and they certainly don't want to start a war along the Canadian border.