No, I don't think so. Maybe in some contexts, but not in all.
It's almost like the specific phrase "I'll be needing that" means "I will start needing that in the future", suggesting you do not need it now or do not obviously need it now.
But in general the -ing in the future just emphasizes the action is ongoing. It's almost never necessary.
This specific phrase is a little unusual, so the best way to learn it is:
1. Understand the basic idea of -ing as 'ongoing'.
2. Look up examples of this phrase (and others!) in use.
The "meaning" to a native speaker is just the sum of all times they've heard the phrased used. What you're lacking is that experience, so if you want to know the "meaning", you just need to see more examples. You're beyond the basic "rules" at this point.