In Jain understanding, a spider is a limited-sensed जीव and does not normally have the capacity to fully understand Tirthankar vāṇī the way a human with proper devotion and right understanding can.

In the samavasaran, Tirthankars’ divine sermon is heard by different beings according to their own capacity and karmic development. So a spider may be present or may receive some influence, but complete understanding of the vāṇī is generally not possible for such a being.

So the simple answer is: not fully, in the ordinary sense.