Not necessarily.
Tropicals, by nature of the climates they evolved in, do not require dormancy. This is why virtually all houseplants are of tropical origin; that and many being adaptable to low light conditions.
No first hand experience with Brazilian rain tree, but I don't believe they require dormancy.
Very many CAN go dormant in a way, and a few may benefit from it even if it's not mandatory. An example is punica - pomegranate - which can be chilled to NEAR (not to, or below) freezing, and will lose its leaves and hibernate for a while. Mixed reviews on whether or not it's beneficial. I've gotten chili peppers to go dormant in winter the same way, and doing so every winter will buy them a few more growing seasons of better health. That's compared to 2 or 3 seasons of continually decreasing production.