As a group, no
Taken all together, the diagonals sit 14 centimeters above their flanks. Five and a half inches. Grid streets sit exactly level. As a generalization about Chicago's bent streets, the myth fails.
Two corridors, emphatically yes
The Green Bay Trail — Clark Street, Ridge Avenue, Green Bay Road — rides a crest a meter and a half above its flanks. The Calumet beach roads in the south suburbs and Indiana do the same. At one-meter resolution, Ridge Avenue in Evanston sits on the spine of the Rose Hill spit, 2.5 m above the yards on either side. The people who named these streets were being accurate.
The famous ones, no
Milwaukee, Elston, Archer, Ogden, Vincennes and Lincoln are level with the ground around them. They bend for other reasons: a river bank, a portage, a plank road's straight line to a distant town. Chicago is flat because it is a lakebed. The streets that remember the lake are the ones on its beaches.
How it was tested
USGS 3DEP 1/3-arc-second elevation reprojected to UTM 16N at 10 m, detrended with a 400 m Gaussian so the regional slope drops out and only local relief remains; one-meter Cook County lidar for the close-ups. The Glenwood (640 ft), Calumet (620 ft) and Tolleston (605 ft) lake stages are rendered as a connected flood — a pixel counts as underwater only if it is hydraulically joined to the Lake Michigan basin, which is what makes Blue Island an island and keeps inland depressions dry. Then every major OpenStreetMap road, sampled every 50 m: elevation under the road minus the mean of six flank samples at 150, 250 and 350 m perpendicular to its bearing, on a DEM smoothed to 60 m so the road prism itself disappears. Expressways excluded — their embankments are ridges of a different kind.
Caveats, honestly
Lake-stage elevations are the textbook values; the real shorelines are tilted slightly by post-glacial rebound. Rail lines and expressway embankments show up as artificial ridges in the relief. OpenStreetMap splits corridors across name changes, so grouping roads into trails was done by hand.
Data
USGS 3DEP elevation · Cook County 2016 QL1 lidar · OpenStreetMap roads and water via Overpass. Lake stages are the textbook Glenwood, Calumet and Tolleston values.