Your transaction (1.00000001 ===> 0.99990000 transfer + 0.00010000 fee + 0.00000001 change) will be valid. But it is not guaranteed that other nodes will pass your transaction. May be yes, may be no.

Modern referral clients do not relay such transactions, because developers hate dust and spam. But there are nodes which relay such transactions and there are miners who confirm them into blocks.

E.g. https://blockchain.info/ru/address/1Fri3h6MtMkjZjYHub4r1N6r5nERWgZXHQ

Your transaction (1.00000001 ===> 0.99990000 transfer + 0.00010000 fee + 0.00000001 change) will be valid. But it is not guaranteed that other nodes will pass your transaction. May be yes, may be no.

Modern referral clients do not relay such transactions, because developers hate dust and spam. But there are nodes which relay such transactions and there are miners who confirm them into blocks.

E.g. https://blockchain.info/address/1Fri3h6MtMkjZjYHub4r1N6r5nERWgZXHQ