I wouldn’t have thought so, but since the Gulliver Nook Miles achievement tracker updates after Gullivarr is here and you still get a rusted part the next day, I do wonder?
I think it counts once you help him find the communication parts. I thought if you only just talked to him then left it wouldn't count, It counts when you have done the task finding the parts.
I was hoping it would count but don’t think it does. It would be nice if it did count.
Also it took me seeing this post to remember I still have to find the rest of his communicator parts. I got distracted trying to get my campsite villager to move to my island.
I'm at the 29th visit for Gulliver and 19th visit for Gullivarrr (I didn't ignore them and completed the task every time) but haven't received the golden shovel yet so I guess not.