Traveling with US iPhone and a UK SIM card

While traveling in the UK, if I swap out the Verizon SIM card in my iPhone 5s with a UK SIM card, and then purchase a UK mobile phone plan, the phone will be assigned a new phone number for as long as the UK SIM is installed. It would then follow that text messages sent to my US mobile phone number wouldn't reach me on the iPhone.

However, should those same text messages reach my laptop though the iMessages app, since it works through ICloud and a WiFi connection?

Likewise, would I be unable to retrieve email from the iPhone, since my Apple account is associated with my US phone number, but still be able to retrieve email through the Mail program on my laptop via a WiFi connection?