The logic you show here proves how well you're picking up Welsh, and how well you're able to make guesses on words you're not familiar with from patterns you've seen before :)
As shown below, wedi priodi means "married" in a similar sense that wedi blino means "tired".
Literally, you're saying "have married/tired" but over time the phrase has become a single word in its own right.
Basically You're right, but in speech i spose it flows a bit more to say someone "is/are married" moreso than "has married"
It is a fundamental rule with verbs in Welsh that 3rd pers. pl. forms are only used where the corresponding pronoun nhw they is explicitly stated. In all other cases where the subject is 3rd pers. pl., the 3rd pers. sing. form must be used. Compare:
Maen nhw’n dysgu Cymraeg [pl. verb]
They are learning Welsh
but: Mae Kev a Gina yn dysgu Cymraeg [sing. verb]
Kev and Gina are learning Welsh
°Gân nhw ailwneud y gwaith ’ma yfory [pl. verb]
They can redo this work tomorrow
but: °Geith y myfyrwyr ailwneud y gwaith ’ma yfory [sing. verb] The students can redo this work tomorrow
(Modern Welsh: a comprehensive grammar, §212)
Would Mae Alys a Sioned yn briod make any difference compared to Mae
Alys a sioned wedi priodi ?
The latter sentence should translate literally as 'Alys and Sioned have married' (present perfect), rather than 'are married' (which sounds as an adjectival predicate). But maybe in Welsh they sound exactly the same, or maybe yn priod is not very common.