Create a Rules link to update a field in a submitted webform
Have a look at what's asked for in the feature request "Expose submission data to rules", status is "Needs review". Here is a summary of it:


  Right now, submission data is not exposed to rules except by way of token replacement or custom php actions. This patch exposes submission data in a "first-class" way.


So if submission data are not even exposed yet (in the current version of Rules), then it might not be obvious (if possible at all) to update such data.

Possible alternative

I'd rather try to come up with some kind of alternative for such hidden field to "record the clicking of such link" (also using the Rules Link module). A possible alternative is to use the Message module to create a message like so:


Date = date the link was clicked.
User target = the user who clicked the link.
Message type = something like "Webform processed via Rules link").
message text = whatever you want and possibly using "Replacement tokens" to have any of the available webform tokens available in your rule included in your message text also.


Since messages are entities, you could add any additional fields you may need to complete such custom logging.