I was just there in July/August. Not impossible at all, it was wonderful!
Weather was totally fine (well, hot and sweaty, as it is in the tropics). Of course it rains, but in 4 weeks we had maybe 2 mornings that were really difficult to bird because of rains, not more.
We made a big loop and passed basically all topographic and climatic zones, and there is not a region I would recommend to avoid.
One down-side is certainly that north-American migrants are absent. Not a big deal for us, as we were new to the region and plenty exciting things to see with the resident birds. On the plus side, summer is main season for turtles (and tourists!) in Tortuguero and Whales in Uvita.
Quetzales don't have their long tails in the summer, but are an amazing sight even without.
Here some impressions: