I use an OBi202 along with a Google Voice number for my home number.
When I use that number for 2-factor text authentication I receive an
Email with the code on my Google Email account. The setup also works
fine with automated voice 2-factor calls.
As for Google Voice once you get things working while in the USA all
they know is that you are on vacation and took your Obihai box with you.
If they cause problems just use a VPN service from where you are
pointing to somewhere in the USA.
You can use he OBI200 to save a little money as it only has one phone
jack where the 202 model has two jacks. The 202 could be configured to
ring one phone for your Google voice number and have the second jack be
used with a European VOIP phone number. Similar can be done with the
200 model but both numbers would ring in on the same physical phone.
With some configuration work you can program the outbound calls to use
the European number for what would be your local calls and it would
route USA bound calls through the Google Voice number.
Of course you are not forced to use Google Voice as the boxes can be
configured to work with just about any VOIP service provider.
If you do go the Obihai route be sure to check online for sales as they
can be had at a big discount from time to time.