Order of Operations in Adobe Analytics

I would not call it order of operations, but theoretically yes, segments are the global filters for a panel that will already filter out some dimensions. Then, if you apply additional filters to a dimension in a free form table header, this will remove additional entries.

the metrics is just the numbers how often the dimension was counted which you can apply additional filters on as well, but these will not affect the shown dimension entries.
applying filters to the metrics in the column heads may affect the ordering of the dimensions though but should not remove items 

Adobe processed the data in workspace from the top down. If there is a segment at the top of the panel it will look at that first (From left to right if there are many). In a table it will again in each column from the top down. If you put a metric at the top then a segment under it, it will find the count of that metric then apply the segmentation to get the final result. it will ten apply the left side of the table depending on how you are looking at the data.