Good morning @Mumpa,
Thanks for reaching out with regards to your device functionality while abroad. Staying connected is important so I'm happy to shed some light on how iMessage works.
The short answer to your question is no. Apple's iMessage works over the internet, so if you don't have active data transmissions, you can't send or receive iMessages, just like you could not send or receive email messages.
However, iMessage does function via Wi-Fi, so you can text with others who also have iPhones and iMessage, even while travelling! You don't have to do anything special to make iMessage work as it should already be turned on in your device Settings.
Hope this helps!
Apple's iMessage works over the internet,
1. Although iMessage works over WiFi (the Internet, for free), there is an option under the iPhone settings for iMessages to be sent (and received) via SMS. If this option is turned on (which I believe is turned on by default), this means that when you are not connected to WiFi (the Internet) you can still receive/send iMessages, however, they are sent as SMS and you will be "billed" for these texts the same way you are billed for texts to/from non-iPhones.
2. You do not need data to sent texts. They are sent via the cellular network, but you are billed according to your plan for texts which could be nothing, or could be 70 cents+/text depending on your plan and where you are.
3. I am on a pre-paid (PAYGo) plan with Rogers and have sent/received texts all over the world, however, I am billed at the texting rate for the country where I am. This can be a fairly large charge per text, (say 70 cents or more for a long text), however, I don't do it much and my texts are short, so I'm perfectly happy paying a few dollars per year on a "per text" basis.
4. When you look at your messages on your iPhone, you will see that they can be in two different colours. The green ones are SMS and are billed at texts. The blue messages you send are iMessages and cost nothing since you were on WiFi (or perhaps Internet/data).
5. I'm not an expert on what triggers roaming charges if you're not on pre-paid for example.
6. Because I don't have data on my iPhone SE, I cannot comment on this exactly, however, I assume that if you have data, you are connected to the internet when a signal is available and you will be billed as "data", whatever that costs on your particular plan. On the iPhone you can go into Settings - Cellular and turn cellular data on or off.
PS. I'm not an expert on this and don't text very much, but I thought the clarifications may help.