Proj.4 documentation about "units" is at
https://trac.osgeo.org/proj/wiki/GenParms#Units
Listing the supported units with cs2cs gives this result:
cs2cs -lu
km 1000. Kilometer
m 1. Meter
dm 1/10 Decimeter
cm 1/100 Centimeter
mm 1/1000 Millimeter
kmi 1852.0 International Nautical Mile
in 0.0254 International Inch
ft 0.3048 International Foot
yd 0.9144 International Yard
mi 1609.344 International Statute Mile
fath 1.8288 International Fathom
ch 20.1168 International Chain
link 0.201168 International Link
us-in 1./39.37 U.S. Surveyor's Inch
us-ft 0.304800609601219 U.S. Surveyor's Foot
us-yd 0.914401828803658 U.S. Surveyor's Yard
us-ch 20.11684023368047 U.S. Surveyor's Chain
us-mi 1609.347218694437 U.S. Surveyor's Statute Mile
ind-yd 0.91439523 Indian Yard
ind-ft 0.30479841 Indian Foot
ind-ch 20.11669506 Indian Chain
Linear units in Proj4 can be to converted into meters with +to_meter parameter but with degrees that is not possible and therefore my conclusion is that +unit=degrees is not valid. Document http://dl.maptools.org/dl/omsug/osgis2004/PROJ4_HandlingCoordinateSystems.pdf says about +proj=latlong that "Units is implicitly degrees" so there is no need to define the units.
Interestingly the documentation of Proj4 javascript port http://proj4js.org/
does have examples where +proj=longlat and units=degrees are used together
proj4.defs('WGS84', "+title=WGS 84 (long/lat) +proj=longlat +ellps=WGS84 +datum=WGS84 +units=degrees");