Rust does not have GC, but it’s not magic. It could help you use less memory, but it depends on the type of the problem.
If your memory usage is high due to frequent allocation and deallocation of lots of objects that GC has to clean up, then Rust will likely have smaller peak memory usage. OTOH if you only need to allocate memory once and then keep it, it’ll be similar.
In Java there may also be an overhead of using objects. If you’re using lots of very small objects (smaller than 16 bytes), then Rust may help you pack your data more efficiently.
So to simplify “What would happen if this program would get ported to Rust” — it could use 50GB or memory, or could need closer to 100GB, depending on nature of the problem.