Does running a pruned node support the syncing of other nodes in the network?
does such a node support the syncing of other nodes in the network?

Nodes that are pruned unset the NODE_NETWORK flag, which means that they don't advertise themselves as a potential source for block synchronization. Nodes won't consider peers without this flag as a potential source for downloading blocks.

In such an early state, before pruning kicked in, does such a node serve the subset of the blocks that it has to the network?

The same flag is not set here either. During sync most nodes are typically at 100% utilization and tend to behave very sluggishly, so they wouldn't be a particularly good source for anybody else.