No. The world's major deserts are predominantly located in continental interiors (rain shadows) or on western coasts (cold-current deserts), not eastern sides.
In the tropics and subtropics, trade winds blow from east to west, carrying moisture from oceans onto eastern continental margins. This creates rainforests (Amazon, Congo, Southeast Asia) or humid subtropical zones (US Southeast, East Asia, East Australia).
Small rain-shadow deserts exist on eastern margins where mountains block moisture: Great Sandy Desert & Simpson Desert (central/western Australia, but eastern relative to some ranges), Sechura Desert (Peru coast—actually western). These are minor compared to the global pattern.
Bottom line: Deserts cluster where moisture is blocked or air descends—mostly interiors and western coasts.