Not bad at all! We normally go that time of year because the brutal heat isn't quite there yet. Also some schools may not be out yet so crowds aren't crazy.
They will be less busy than later in the summer, but the parks are busy pretty much year round now. You wil still want to book your dining and fastpasses as far in advance as allowed.
We finally decided to do the first 1 1/2 weeks in June as well (had debated mid August)! Our kids our done with school June 1 and are flying out that evening on a redeye. Now if I can get confirmation on our accommodations!!
We usually go a soon as school is out locally which is the first week of June. We have found it to be somewhat crowded but not really packed. We go that first week because many schools are not out then. As others have said, crowds really ramp up starting with the second week in June. If you are going in June 2018, watch for a bald guy wearing a "Grumpy and Proud Of It" t-shirt. Wave when you go by...