texture memory question - colour tinting a single texture multiple times?

I’m working on a project for mobile and texture memory is becoming a big issue. I’m thinking of rather than using multiple textures but to share a single texture over multiple assets with a different colour tint on it.
Am I right in thinking this will reduce the memory foot print as I have heard this might brake batching and force the app to generate multiple versions of the source texture?

It will not generate multiple versions of the texture. It will create a new material for each color, which will prevent batching from working.