Yes, weird noises from the undercarriage will happen during updates. I’m pretty sure once your Model 3 notifies you that an update is available said update has already been downloaded and is just waiting for the install to kick off. I doubt it even cares if it has a cell signal at this point.
I’m sure your Model 3 did update successfully. This was my 6th update in just 8 weeks of owning my Model 3. Of those 6 updates only one had an installation issue, which my Model 3 did display an error message about. That was easily fixed by Tesla, they simply pushed the same update to my car again and the second install attempt was successful.
My advice to you is to just start the update and do something else while it installs. If it has a problem installing your Model 3 will tell you. Even if it did encounter some sort of issue during installation there is likely nothing you’d be able to do about it.
And I’d just like to complain yet again on how it doesn’t even show you what version it is until the update is complete. This seems like pure insanity from an IT perspective.