Well, that's gonna depend on the age and inner surface of your tub. I used to dye my hair hot pink, and that was all hell on a tub compared to tea. Bathtubs can be washed with cleanser and bleach, which removes most staining, but as with all dyeing, YMMV.
If you can find some sort of cooking pot that is large enough for your curtains, you can do it as a stovetop dye, but almost universally, curtains are too big for that.
If the fabric is too crowded when dyeing, you will wind up with a subtle crinkle pattern throughout, as the folds resist the dye. Done purposely, this is a way of adding visual texture, but most people want even dyeing.