Does a gauge recommendation refer to pre- or post-washing dimensions? I'm following this pattern to make a sweater. For the gauge requirement, it states:


  17 stitches and 31 rows = 4 inches in Seed Stitch


Then the schematic shows the front/back panels having a width of 20" each, and the pattern calls for 98 stitches each. But that comes out to 98 / 20 * 4 = 19.6, which isn't 17. It seems like this could mean the 17" measurement is unwashed, if the fabric is supposed to shrink.

But the pattern also says:


  Seed stitch will grow when blocked. If you are concerned about the length, measure your gauge in seed stitch from a washed and blocked swatch and calculate number of rows necessary to achieve desired length after blocking.


Finally, a rough comparison of the sleeve length in the schematic (18" including cuff) with the pattern (1.5" cuff + 127 rows) would give 127 / (18 - 1.5) * 4 = 30.78, which is roughly the suggested gauge of 31, suggesting the fabric would be expected to neither shrink nor grow during washing.

My gauge swatch before washing is roughly the recommended 17x31, but given the above discrepancies I'm concerned that the measurements in the schematic won't be accurate.

Should I consider adjusting my needle size to achieve a washed size of 17x31? Or should I expect the schematic's measurements to be accurate even though they seem to disagree with the gauge recommendation? Are there any other techniques I can use to validate the sizing before I get too far into the pattern?

(This will be my first serious blocked garment where the sizing actually matters, so I'm also not sure how much leeway I will have to adjust the size during blocking. If it matters, the pattern recommends 2–4" positive ease.)
I couldn't follow your calculations but the way I do it is to convert the gauge to stitches per inch which is 4.25 in this case. Then I divide 98 stitches by 4.25 stitches per inch to get about 23 inches. The row gauge is 7.75 rows per inch. 

But more importantly, the pattern is an aran type sweater which means lots of different cables and stitch patterns across the width. The designer is saying that if you get 4.25 stitches per inch in your gauge swatch in seed stitch, you'll probably get the right size garment. IIRC cables shrink the width as they build up the 3d-ness. I've seen some designers give gauge swatch knitting directions that incorporate all the stitches and directions of knitting in the garment but that is quite rare.

I assume you are knitting this in wool which can stretch in blocking if you encourage it to do that.

It is my understanding that gauge swatches are always interpreted as washed and blocked sizes and they usually say so.