Yes, this is very likely. Especially with someone who has been wrong on every foreign policy issue over the last 40 years as president in the US. I can all but guarantee that this would not be happening today if Trump was president.

NATO was intended to deter Russian aggression toward Europe, and even though Ukraine is not part of NATO, invading Ukraine is a signal to NATO that eastern NATO nations are next. Unfortunately, the US has effectively been subsidizing European defense since during WW2, and NATO members other than the US are not serious about defending NATO.

As it stands, now Russia would suffer major losses in invading Ukraine, even if NATO and/or the US does not get involved. The people of Ukraine are against being invaded by Russia and the US, under the Trump administration had fairly decently armed Ukraine. So even if Russia does invade Ukraine, it is not a given that Putin survives politically (he is a dictator, but even dictators can only do so much and still stay in power).

Assuming Russia invades Ukraine, what happens next, will largely depend on Germany and the rest of Europe. If the Germans are willing to shut down the Nordstream pipeline and impose strong sanctions on Russia, I don't think Russia will advance past Ukraine. However, if Europe is unwilling to force Russia to pay economic penalities for an invasion, Russia will likely quickly expand Westward.