The short answer
Yes — plain cooked pasta is safe in small amounts.
Why
Plain, cooked, unsalted pasta (wholegrain is best) is a safe, gentle food many budgies enjoy. No sauce, salt, oil or seasoning.
How to feed it
Offer a small piece of plain cooked pasta, cooled. Cooked is easier to eat than raw.
How much & how often
A small amount occasionally.