No. While a rhombus is a quadrangle which cannot have a right angle, that, in itself, is not enough.
A rhombus for example
rhombus
Most quadrangles do not have right angles. A rhombus is one example.
A rhombus.
rhombus
A rhombus
a rhombus or parrellegram
A rhombus.
A rhombus.
You are a rhombus.
You are a rhombus.
Rhombus!