not exactly; arabia isn't covered in shrubbery in the literal sense; the flora tends to be herbs, some grasses, and small bushes. and the floor isn't typically rock, its more a gravely sand mix, especially to the east.
there are however parts of western arabia that are covered in rocks as some of you envision; they're called 7arraat; they the remains of old dorment volcanoes (they have erupted several times in the last 2000 years).
a 7arrah (at least I sssume so, from the rocks):
http://www.photoforum.ru/f/photo/000/036/36344_84.jpg
some parts are even suptropical; this is so on jabal-3umaan and parts of 3aseer (in oman and SW saudi arabi/NW yemen) respectively. here is a valley near jabal 3uman:

these are from 3aseer, around Abha (warning: will violently smash stereotypes regarding the arabian peninsula):
tihaamah (on the west coast, ahead of Hijaaz) is a marshy place, with plenty of sand dunes, a few scatered oases, and bad to sail near.
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