No. This is not true. I just tested it myself. Adding more leech increases the healing for sure (even when you are NOWHERE near the cap).
The character has 279 HP. The leech cap would be 62.78 at 5% leech and 69.75 at 10% leech.
This character's auto attacks deal 52 damage. By your explanation, this SHOULD heal me for 26 HP (since all leech does, according to you, is increase the cap). 26 is nowhere near EITHER cap listed. If what you're saying is true, then adding ANY amount of extra leech would simply do nothing for the character.
In this video, I show what happens when you have 5% leech. Then I equip another mosquito bug card to get another 5% leech (for a total of 10%).
https://youtu.be/Zq63C39qyw0
As you can see, at 5% leech, each hit for 52 heals me for 6. While at 10% leech, I was healing for 7+5 (12). As you can see, I doubled my leech and literally doubled what I healed. So clearly how much leech you have matters, even when you're nowhere near the cap.