Dboy
Yes, you need (a stable) internet connection to add the eSIM.
Sometimes it doesn't obtain the correct APNs or need more time (e.g. 15 min) connected to the roaming network.
Not sure if you need this:
Note that if the eSIM installation process does not progress past the "Checking network info..." stage despite having a stable Internet connection, you may need to call the USSD code ##4636## and then enable DSDS in the menu that is presented.