No, it’s just used for those consonants. It represents h in certain situations. For example teach (house) could be written as teaċ. The vowels can have fadas (acute accents).
H does exist in Irish, The Séimhú (dot) is mainly used as a replacement for h when a word is modified, eg: bean (woman) an bhean or an ḃean (the woman).
The old alphabet had only 18 letters —
a b c d e f g h i l m n o p r s t u
— although some of the other latin characters now appear in imported words.
Hope that makes sense.