Will the western world let Ukraine use the provided weapons on territories after possible Russian annexation?

Western partners provided Ukraine with weapons under the principle "not to attack the Russian territory explicitly" and "as many weapons as Ukraine can "swallow."
Today after sham referendums on Ukrainian territories, Russia is about to proclaim territories as parts of Russia. Ukraine is not going to surrender. After a recent successful counter-attack, Ukraine liberated more than 6000 thousand square kilometers of its land in the Kharkiv region. Only 6% of this region remains under Russian occupation. It seems like nothing won't stop Ukraine from bringing back its land. But will the west be scared to give more weapons when Ukraine liberates the territories that might be proclaimed Russian?

According to US secretary of state Antony Blinken, the USA will continue to support  Ukraine.
"We and many other countries have already been very clear: we do not recognize and, in fact, we will never recognize the annexation of Ukrainian territories by Russia... Ukraine has the absolute right to defend itself throughout its territory, in particular, to take back the territories that were illegally seized by Russia in that or some other way," Blinken said.

Blinken emphasized that pseudo-referendums do not change anything for the Ukrainian territories seized by Russia.

"Ukrainians will continue to do what they need to return the land taken from them. We will continue to support them in these efforts," the US Secretary of State said.
It inspires a lot of hope and gives more strength to the people of Ukraine. But will Ukrainian partners remain so adamant in the wake of recent increased nuclear threats? This is one of the most relevant questions of the war today.