Buying a cheap, lightweight stroller is definitely a good way to know if it will work for your situation. Depending on what types of activities you’ll be doing first on the trip and where you’ll be staying at the start, it might be worth considering buying the stroller before you leave for a few reasons.
First, you’ll be able to take advantage of having it for the entire door-to-door trip. There’s of course reasons why you might prefer to buy one after you arrive, but in our experience it was a huge help at the airport. If you have one before you leave, you’ll have more to go on to better figure out if a stroller will work for you. Things like being able to fit in the car, how you carry it with other baggage, how you find taking it through security, etc. They might seem small, but we found these things became valuable to know – the longer you get to test it out, the more you’ll know if it will work for you.
Second, it will provide them their own space for them to sit and relax (and possibly sleep) which if you get delayed – or like us you like to leave a lot of time to avoid any stress – will be really helpful. This of course applies whenever you have a stroller, but at the airport we found our daughter was much happier having a consistent place to herself. It obviously depends on the child, but we always made sure she was in the stroller as soon as we arrived. If we had to discuss something with airline staff, figure out directions, or get stuff from our bags, we were able to focus on that knowing she was safely buckled in and comfortable. When she was younger, we made sure she had a toy (attached to the stroller) and when she was older she would happily sit and read a book (she is a bookworm). It also has the advantage that if you’re trying to find somewhere to sit, the stroller can act as an extra seat so you only need find space for yourselves if the gate or seating area is really busy.
Third, you’ll save yourself some time when you are wanting to get out and explore wherever you’re visiting. If you know the type and location of stores at your first destination then that’s great of course, but if you are unfamiliar with the place you might spend a long time searching for somewhere to buy it. Also, if you’re dealing with any jet-lag or time zone adjustment (or perhaps even travel sickness) that could add hassle and stress, as well as taking up time you might otherwise want to use to explore.
Lastly, having a stroller at the airport will allow you to become familiar with the gate-checking process. Generally, we found most airlines to be very good about boarding and we always made sure we boarded earlier when we could. We found we needed a little practice to understand how we needed to do things (e.g. checking her stroller, boarding, then installing her car seat), so the more you can understand now, the easier subsequent trips will be. We were lucky that we learned fairly quickly what worked for us and that our daughter naturally travels fairly well, but setting up a routine helped us and our daughter a lot (by about 8/9 years old she was buckling herself in the stroller).
If you already have an idea about the sort of luggage you’ll be taking, you're confident with your plans for the airport, and you know your first destination well, then it of course makes sense to buy a cheap and light stroller once you arrive. This is only our experience of course, but when we figured out bringing a stroller made things much easier we invested in a really good quality one (two in fact as we got a larger one as she got older) which also helped knowing it could withstand the traveling. It’s different for every family of course, so be prepared for it taking a few trips before you know what works best for you. Hopefully this is helpful and have a great trip!