Thanks asking!
Re: "You want to convert the vertices defining your line to points and then calculate the length of the line up to that point into an M-Value field?"
Actually no, I don't want to convert the vertices to points. I want to update the M-values that are stored in the vertices of the polyline. M-values are similar to the X, Y, and Z coordinates of a given vertex...X, Y, Z, and M are stored in the SHAPE column of the feature (not in numeric fields/attributes).

"Are you actually using linear referencing or was that just an example or are the vertices just vertices along a linear feature?"
Yes, we're actually using linear referencing. We have a CONSTRUCTION_PROJECTS table (non-spatial) that has EVT_FROM and EVT_TO fields. We use that table to plot construction events along portions of lines via a linear referencing event layer (more info here).
In our case, our M-values are always exactly the same as the cumulative distance of the line. If we could, we wouldn't even use the M-values, and just use the length of the line. But I don't think that's possible. So we want to find a way to automatically set the M-values to the cumulative length of line. If I can figure out how to do it with SQL, then I'll use that SQL to create a Oracle trigger that will update the M-values if a user creates a new line or edits the shape of an existing line. That would be a lot better than relying on a user to do it manually when creating or editing a line:

Cheers.