Can the Apple Watch Ultra do this?

You need to hold & aim the iPhone 14 towards the satellite signal to connect, so it’s not possible to do this with the watch alone. Ultra does however have SOS and crash detection etc.

see: Apple Watch - Compare Models to see the specs.

To the best of my knowledge using the information provided, no.

Emergency SOS requires a cellular connection or Wi-Fi Calling with an internet connection from your Apple Watch or nearby iPhone.

Apple Watch Ultra (Cellular), Apple Watch Series 8 (GPS + Cellular), and Apple Watch SE (GPS + Cellular) can use a cellular connection for Emergency SOS. To use Emergency SOS on an Apple Watch without cellular, your iPhone needs to be nearby. If your iPhone isn’t nearby, your Apple Watch needs to be connected to a known Wi-Fi network and you must set up Wi-Fi Calling.