Define "growth", please. Are you talking about the gross extension of length on leaves and shoots and such, or branch/trunk thickening? Or perhaps basic metabolic and cellular functions such as DNA and cell replication, manufacturing of proteins and cytoskeletal and extracellular structural molecules, manufacturing of storage molecules and structures, etc? Is the "spending of energy" growth? And what energy is "spent" in photosynthesis, which is actually the capturing and retention of energy (and matter) in a net positive reaction?
IMO, photosynthesis, which is a process of accumulation of both energy and matter, is as much "growth" as anything else a tree does. I believe a tree, except when very dormant, is ALWAYS in a process of growth of one sort or another. If you just mean shoot and leaf extension and such, that's another matter.
Funny, but a fast-growing species would be the easiest way to tell. I have ficus and trident maples that will show new extension growth and leaf growth by the end of the day from what I have seen in the morning.