I have a first generation 2i2, I believe, and it is a noticeable improvement from trying to plug HD600 into a random audio jack which were obviously not able to

I have a first generation 2i2, I believe, and it is a noticeable improvement from trying to plug HD600 into a random audio jack which were obviously not able to actually drive them properly in general. You should be fine dropping the additional headphone amp, which I think beyond the Scarlett or similar audio interface will perhaps be different depending on the amp, but not clearly making up for a deficiency in interface power.