The time for substrate exposition,(frequently) it is very short and the reaction is developed at room temperature so, very little evaporation occurs during this step. Any way, you can cover your ELISA plate at anytime you like.
When removing the plate sealer you might "splash" some of the substrate into different wells, thus ruining your results. You need to incubate the substrate in the dark because it is light sensitive.
Covering may cause contamination and covering doesnt ensure perfect masking for light, also it may result into handling errors. So using a dark space is very easy to avoid all such errors.
I experimented both methods there was no observed different. But I prefer open plate to covered one. As Mr. Sullivan mentioned you might splash it. So you can cover your plate at any time you like as Mr. Otero said.