The answer is Yes! The standard starting position for Chess is one of the 960 possibilities in Chess960!

It happened in a game today, and out of the 4440 Chess960 games on PlayStrategy it has been selected on 4 occasions (which is about what you would expect as 4440/960 = 4.625).

Also notably, the standard Chess starting position was selected twice in the 2024 MSO Chess 960 tournament (out of 138 games): playstrategy.org/swiss/XFZGdmy3