Eh no, the branch of Celtic family is called Goidelic, the use of term "Gaelic" originates in Scottish context as a "neutral" word to use in English instead of pre-existing "Scots" term of "Erse" (which literally means Irish). Basically it was politically-correct word to differenate language in Scotland from Ireland.
The term "Gaelic" was thus never applied in Ireland until the 20th century and even to this day if someone calls the language "Gaelic" in Ireland it's generally due to deep seated animosity towards the language. In comparison in English state papers from the 15th-19th century for example specifically call the language "Irish", which reflects fact that it was majority language in Ireland until about 1800.
In modern day context the only people you tend to hear calling the language "Gaelic" are american's, in Ireland as pointed out above the word has a derogatory context.