Usually, yes. Two different things are involved: the text messages that bring your security codes, and the bank app itself.
Codes sent by text go to your own number, on your own SIM. Keep that line switched on in your phone's settings while the travel eSIM carries the data, and the codes keep arriving. Your home carrier may charge for texts received abroad — its roaming terms say.
The app sees the country your connection appears to come from — the IP location, which each plan names where the network states it. Some banks question or block a login from a country they do not expect.
Where it matters, tell your bank before you travel, or choose a plan whose IP location suits your bank: "Choose your IP" lists the IP locations a destination is sold with.
How a bank reacts is its own security decision, so we cannot promise it. If the app still refuses, the bank's support line can usually unlock it, and a call to your own number still reaches you.