In this case, I do not think that the applications on the nodes need to have their start times randomized, because the Wi-Fi channel access mechanism (DCF) will randomize the access.
If there are at least two nodes trying to access the channel at the same time because they have a backlog of packets queued, there will eventually be a collision in the channel access when nodes happen to pick the same random backoff value, but Wi-Fi will detect this via a missing acknowledgment and resend the packets with different random backoffs, and they will (usually) be successfully retransmitted at some point in the future.
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