Data in a geographic coordinate system is treated, in a sense, as two-dimensional, at least to the point that there are edges, just as in a projected coordinate system. Generally, the edges are at -180/+180 for the east–west extents, and -/+90 for the north–south extents. These extents are called the "horizon" of the coordinate system.
When ArcMap displays data in a geographic coordinate system, it is shown as two-dimensional. Part of the reason for this is that there is a discontinuity at the +180 and -180 meridians. Although they represent the same line, they are relatively far apart mathematically. Identifying and handling features that cross this discontinuity would have a performance impact.
In a geodatabase, a feature that crosses an edge will be clipped to the horizon. If you are editing features in ArcMap, the data frame's coordinate system will affect what happens to a feature that crosses the +/-180° line. If the data frame is using a geographic coordinate system, that is, the +180 and -180 lines are separated, a feature that crosses outside the horizon will be clipped to the horizon. If the data frame is using a projected coordinate system, with the +/-180° line inside, a feature that crosses it will be split into multiple parts.
Some clients instead use a 0–360 or -360 to 0 longitude range, although this does just move the issue to the Greenwich meridian. It's also possible to store data in a projected coordinate system that is centered in the Pacific, but again, that will mean that there is a "break" somewhere else in the world.