Definitely not. Simple services like ipchicken.com will show you're using an IP address local to the roaming provider that you're using. If you're travelling far enough, you can try accessing local services vs home-country-services and compare loading times. Or better still, just ping various services that are local or in your home and compare the actual latencies.
I guess then that it depends on the local carrier, roaming carrier, and the carrier agreements in place. Probably not safe to say one or the other always happens definitively.