After installing the package Dehydrated, there is no chance to see the logs within menu System Logs in WebIf. Currently Deyhdrated writes to stdout and as far as I know, there is no possibility to get the output into /var/log/messages by default means. Do you see any chance of getting the output into the WebIf?
I have had a look through the dehydrated config file and the dehydrated script itself and there is nothing anywhere related to logging. The only option that would be left would be to redirect all stout/stderr to /var/log/messages as part of the fcrontab command that would be used to run the script as required. However, looking at the dehydrated script, that would not be structured in any way, ie would not have the date time hostname etc sections that other stuff does. You could redirect all the stdout/stderr to another log file in /var so that the info is at least collected. So I believe that the answer is that there is no easy way to get it available to be seen in the System Logs section of the WUI.
As there is no logging available from dehydrated then the requested option can not be implemented.