Why not use a ground drain, i.e., landscape drain, to carry the temporary water away? We use them and they work just fine to carry the water to the curb.
To the original question? YES. The standing water will saturate the substrate soil so stay off the walkway when it is wet! Simple? I get the sense these pavers are NOT cemented.
Ultimately, your problem is standing water. Fix that problem and you are on your way to being done.