Why to assume if you can check the facts?
See the list of <wcscrs:crsSupported>
from http://demo.opengeo.org/geoserver/wcs?service=WCS&version=2.0.1&request=GetCapabilities.
By looking at offsetVectors from http://demo.opengeo.org/geoserver/wcs?service=WCS&version=2.0.1&request=describecoverage&coverageid=nurc__Img_Sample you can get the native resolution. It is a bit hard to interpret even if you study WFS 2.0 standard https://portal.opengeospatial.org/files/09-110r4.
Fortunately you do not need to care about that because native resolution is the default. You must only select your region of interest with &subset=
parameters
http://demo.opengeo.org/geoserver/wcs?service=WCS&version=2.0.1&request=getcoverage&coverageid=nurc__Img_Sample&subset=Lat%28%2220%22,%2230%22%29&subset=Long%28%22-100%22,%22-90%22%29
The end of the request without url-encoding:
&subset=Lat("20","30")&subset=Long("-100","-90")
Check what you get with gdalinfo:
gdalinfo nurc__Img_Sample.tif
Driver: GTiff/GeoTIFF
Files: nurc__Img_Sample.tif
Size is 142, 166
Coordinate System is:
GEOGCS["WGS 84",
DATUM["WGS_1984",
SPHEROID["WGS 84",6378137,298.257223563,
AUTHORITY["EPSG","7030"]],
AUTHORITY["EPSG","6326"]],
PRIMEM["Greenwich",0],
UNIT["degree",0.0174532925199433],
AUTHORITY["EPSG","4326"]]
Origin = (-99.965403825025433,29.979242474916386)
Pixel Size = (0.070036907426246,-0.055867725752508)
Metadata:
AREA_OR_POINT=Area
TIFFTAG_RESOLUTIONUNIT=1 (unitless)
TIFFTAG_XRESOLUTION=1
TIFFTAG_YRESOLUTION=1
Image Structure Metadata:
INTERLEAVE=PIXEL
Corner Coordinates:
Upper Left ( -99.9654038, 29.9792425) ( 99d57'55.45"W, 29d58'45.27"N)
Lower Left ( -99.9654038, 20.7052000) ( 99d57'55.45"W, 20d42'18.72"N)
Upper Right ( -90.0201630, 29.9792425) ( 90d 1'12.59"W, 29d58'45.27"N)
Lower Right ( -90.0201630, 20.7052000) ( 90d 1'12.59"W, 20d42'18.72"N)
Center ( -94.9927834, 25.3422212) ( 94d59'34.02"W, 25d20'32.00"N)
Band 1 Block=142x19 Type=Byte, ColorInterp=Red
NoData Value=0
Band 2 Block=142x19 Type=Byte, ColorInterp=Green
NoData Value=0
Band 3 Block=142x19 Type=Byte, ColorInterp=Blue
NoData Value=0
Pixel size seems similar to offsetVectors so yes, we got the native resolution. Study the standard and you will learn how to get data in other projection but you can't really get the native resolution and warped image at the same time. You must select one or the other.
Hand writing WCS GetCoverage requests are not fun but at least then you know what will happen. I do not know how well this QGIS plugin works http://plugins.qgis.org/plugins/QgsWcsClient2/