Sure, it's possible, but there are issues you need to take into account. For one thing, as your dome sits on the bed of the mill, the top surface is pretty easy to cut, but as you move down the slope it becomes more difficult, because your pointed engraving tool won't engage with the surface - you'll be cutting on the side, if at all. So for basic geometrical reasons, a 3-axis mill will always have trouble doing this.
A solution you might consider is a 4th rotary axis. If you mount your dome to the rotary table sideways, this will enable you to engrave the sides - but not the top, since it is now in pretty much the same position as the sides were before. So you'd need to break up the engraving process into two parts; one for the top, then refixture it and do the sides.
Of course, if you didn't want to do that, or it didn't work with your design, there is another way. You can use a 5-axis mill, which tilts either the spindle or the work so that the surfaces you want to cut and the tool are brought together at the proper (perpendicular) angle. All it takes is some hardware, some software to go with it, and some figuring it all out...
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