it would always appear grey to you?

Not at all. This is a common misconception about colorblindness because the name is kind of a misnomer for the majority of people who are colorblind. There are no colors that I am actually blind to, that I cant see or appear grey to me (except grey, of course). The only way you see some or all colors only in greyscale is by either having a defect in the visual processing of your brain or by missing one or more of the color sensing structures of the eyes. These structures are called cones. They come in red, green and blue varieties, and react to different ranges of light frequencies that causes us to see different colors.

My green cones still trigger for green frequencies for me exactly as yours would for you, so I do see colors, including green. But my colorblindness happens because there is a structural difference in my green cones that shifts the range of frequencies that trigger them towards the frequencies that trigger my red cones too. Because of this, there is a sizable range of color frequencies that trigger BOTH my green and red cones. Everyone has a little overlap, but mine is much larger than the normal overlap in non-colorblind people. When that happens, I still see colors. But instead of distinctly green or red colors, what I see is more muddled and brownish than what you would see. It's because I'm basically getting mixed signals from my cones. There are also frequencies of light that are outside of this overlap that trigger only either my green or red cones, and so those colors do look distinctly and vibrantly green or red, even to me.