We are adding a new 480V panelboard to a facility that has already had an arc flash study performed. In order to label our new 480V panelboard, and assuming that the arc flash study is still accurate, can we use the first upstream transformer as a starting point for our calculations for our new panel?

Yes and no.

Adding reactive loads changes the available fault current for the whole system. Most of the time this has a "barely moves the needle" effect. But not always. This may require changing existing labels upstream of the new loads.

I agree with Pauleng. The proper way is to have it studied or calculate the IE.

Depending on the software and who did your study, it should be a simple matter to use the entire system model and add the new load information.

As PaulEngr mentions this new load information can affect equipment upstream, mostly on the shared secondary of the transformer.

Depending on the size of the transformer and load you are installing, the evaluation should take into account the transformer protection in case this needs to be modified to accept the new load, and prevent nuisance tripping.