No, the i in i mynd is part of something else, like a pronoun. Welsh uses verb-nouns which all mean to something. Mynd to go; gwneud to do; bod to be.

Dw i I am / I do

'n shortened form of yn

mynd to go

i to

yfed to drink

dw i + yn + mynd = I am going. Placing yn between a pronoun and a verb-noun has the same effect as placing -ing at the end of an English verb (go becomes going )

i + yfed = to drink. The to in this sense is same as in English when we'd say I am going to, it is not part of the verb-noun to drink.

So, Dw [verb] + i [1st person singular pronoun] + yn [compliment marker] + mynd [verb-noun to go] + i [to] + yfed [verb-noun to drink] = Dw i'n mynd i yfed I am going to drink.

Also, removing the "going to" part and leaving Dw i'n yfed I am drinking. Again, we have yn + verb noun = verb + -ing.

Replacing yn with wedi would change the sentence to Dw i wedi mynd i yfed I have gone to drink.

Or you could say Dw i wedi yfed I have drunk.