While it’s debatable whether Article 5 would extend to members’ troops in third countries like Ukraine, it would be a moot question in the scenario that nuclear-armed France and/or the UK participate in a “coalition of the willing” there since that's enough to lead to nuclear brinksmanship if they clash with Russia.
Romanian President Klaus Iohannis said that neither NATO as a whole nor his country in particular will intervene in Ukraine but left open the possibility of others doing so on their own. According to him, “Troops cannot be sent to Ukraine under NATO’s mandate because Ukraine is not a NATO ally. But in general, if Ukraine has bilateral agreements with a certain state in any sphere, these issues are a matter of bilateral relations. Romania will not send soldiers to Ukraine.”
It's these legal means through which a “coalition of the willing” could be assembled to this end, possibly led by France whose president was the first to publicly propose this and including Germany and the UK, whose countries have also signed “security guarantees” with Ukraine. The Baltic States would also likely participate after they supported the French leader’s suggestion, while Poland might get involved too if it receives American approval for this mission like its President and Prime Minister seem to be seeking.
While it’s debatable whether Article 5 would extend to members’ troops in third countries like Ukraine, it would be a moot question in that scenario since the participation of nuclear-armed France and/or the UK is enough to lead to nuclear brinksmanship if they clash with Russia there. This is all the more so if America approves of their intervention or at least doesn’t try to stop it, in which case it might back them up, possibly even to the point of threatening to use its own nukes if the fighting doesn’t stop.
The pretext upon which Biden could do so would be the one that he once again referenced on Tuesday about how “Russia won't stop at Ukraine. Putin will keep going, putting Europe, the United States and the entire free world at risk”, but which the Office of the Director of National Intelligence refuted. This Cabinet-level position that oversees the US’ Intelligence Community published a report last month that was only just publicly released this week assessing that Russia has no intent to go to war with NATO.
Unless he goes back on his repeated pledge that American troops won’t fight on the ground in Ukraine, which he’s unlikely to do because of how sensitive this issue is during the presidential election season, then participating in nuclear brinksmanship to support NATO allies in Ukraine would be very polarizing. The risk of sparking World War III by miscalculation just to support the Brits, French, Poles, and whoever else could turn the public against him and therefore return Trump to the White House next year.
From Biden’s self-interested political perspective, it would be better to force Ukraine to accept its de facto Korean-like partition along whatever the Line of Contact (LOC) between NATO and Russian forces might be by then, after which he could campaign on having “averted World War III” instead of risked it. That could also take away the appeal of Trump’s pro-peace platform since the hot phase of the NATO-Russian proxy war in Ukraine, which is really an undeclared but limited hot war, might end by November.
For this sequence of events to happen, he first needs to approve the incipient “coalition of the willing’s” intervention in order to give them the confidence to get openly involved, and then Russia would have to break through the LOC to set the most kinetic phase of their plan into motion. Seeing as how the Ukrainian Intelligence Committee already warned that the LOC could collapse, all of this might happen sooner than later, which would briefly spike the risk of World War III but then reduce it afterwards.