In principle yes for the concept of linear drivers, but I don’t think there is a led with such a low Vf. In practice 7135 also have a bit of voltage loss of their own, so the battery voltage has to be a bit higher than what the led requires. AFAIK they can’t handle more than ~5.5-6V without modifications and as Lexel said, they need a minimum voltage to work as any electronic component.
7135s adapt their resistance automatically to try to keep the current constant, so they don’t need to be finetuned for the Vf range of each led. The Vf is a function of (desired) current or in other words forward current is a function of the voltage that reaches the led, for example a led could take 700mA at 3.0V, 1050mA at 3.2V and 2800mA at 3.6V. If the battery is at 4.0V a driver with 3x7135 will transform the extra 0.8V into heat to keep 1050mA, one with 8x7135 will only need to transform 4.0 - 3.6 = 0.4V to keep current at 8x350 = 2800mA. When the battery (counting losses) goes below such voltage the current will fall accordingly. See for example this test by djozz for the Vf curves of several white leds (the lines in a lighter shade are Vf as function of current, the solid colors are output in lumens).
If you want to run a led with one or two 1.2V batteries you need to use a boost driver. They increase the voltage to what is needed. I don’t really know much about boost drivers. AFAIK small boost drivers can’t handle much current but they may be able to handle 1A output current.