Well, not a much as in July/August, but a lot compared to January.
As Easter is so late this year, free days in May will be plenty. So expect some more pilgrims than last year.
(Costa Camino Portugues 1.580 (3,89%) vs. Portugues-Camino 8.916 (21,93%). Peak months 2018 had about 2500 vs 11000 pilgrims.)
Many leave Porto on the coastal variant, so the first impression might be "it's full". After Vila do Conde it should be "some company" during the walk and almost full at the albergues. Apart from the albergues there is plenty of other type of inexpensive accomodation (<20€pP), don't worry.
Daylight times in early May will be perfect for leaving late in Galicia (7:30-21:30h) At least no reason to leave at 5am, after waking up anybody else in the albergue.