I think it could have.
The early phase of the war, when there was a lot of motion and the successful and then failed counter-attacks were very similar to what war planners thought might happen maybe 1000 miles or so miles west, at the Fulda or Suwałki Gaps. US Army manuals circa the 1980s (I have a collection) quote a lot of material from Russian Armed Forces manuals describing how their defensive lines work, how they expect to do maneuver warfare, etc.
Back then there were many "red lines" crossed by both sides, particularly the use of US-supplied weapons to attack targets on Russian ground, that hypothetically could have been cause for a nuclear war. Those lines got crossed, there was no nuclear war, it's hard to believe it's going to happen now.
The war is now in a frozen state where the Russians gain ground at a glacial rate and it seems unlikely that Ukraine is going to get very much terrain back any time soon. So some kind of escalation seems unlikely, rather steady attrition.
The scenario where China invades Taiwan and the US tries to organize resistance from the Philippines and via a carrier group and China takes a nuclear shot at a carrier group is more believable, particularly as we become economically decoupled.
WWIII need not be nuclear. The US and Russia have fought proxy wars for 80 years at this point without bringing out the nuclear weapons; certainly there's a bigger chance of them coming out in case of direct fighting between nuclear states, and nuclear war would be a big deal, but a conventional world war would be a big negative event regardless.
In terms of sending equipment it's already happened. We just haven't sent manpower. Ukrainians want to fight to defend their country, whereas Iraqis (say) couldn't agree on what exactly they want to fight for.