No... Welsh onions do not originate in Wales, but Asia where they are widely used in many forms
Also referred to as green or bunching onions, and scallion (as are various other Alliums)
depending where about in the world you are, indeed they are in much demand from the West Indies to South Korea and Japan.
An essential member of the perennial onion tribe,welsh onions are available all year round and can deal with whatever the weather throws at them be it hot or cold, they will grow anywhere so long as there's plenty of sunshine and form a large clump in time, producing large pompoms of flowers early in the summer.
Generally they are used like a largish spring onion, providing plenty of green for your salads especially in winter, and flavour for stir fries and stews alike, always giving generously if you can give them a bit of space in your veggie patch.