My initial thought is no:

When mastadon servers share a link between themselves, they are all up at the same time and so they all rush to get a preview at basically the same time.

I imagine most users and their clients will pick up the shared link at different times, offsetting the load. So my hypothesis is that it is the mastadon servers that cause this, not the clients and therefore this will not have an impact on Nostr.

It would be nice to get a confirmation by a webmaster though.