In short answer: No.
As far as I know, the AzureWebJobsDashboard storage account is primarily used by Azure WebJob SDK to store logs from the WebJobs Dashboard. This connection string is optional and is required only if you are planning to use the dashboard for monitoring WebJobs.
The WebJob runtime creates two containers under this storage account with the names ‘azure-webjobs-dashboard’ and ‘azure-jobs-host-archive’. The azure-webJobs-dashboard container is used by the WebJob dashboard to store host and execution endpoint (function) details. Azure-jobs-host-archive is used as an archive for execution logs.
The webjob SDK doesn't support store the log to the table.
If you still want to log the information in the table, I suggest you could not set the AzureWebJobsDashboard connectionstring and write some codes in your web job function to store the message to the table storage by yourself.
Update:
According to your posted article, if your web app enables the web app diagnostics logs' application logging as below, it will automatic write the webjob logs to the azure storage account.
But application logging to the table storage feature has removed the new portal.
If you want to enable it, you should use powershell.
More details, you could refer to below steps:
1.Create a table to store the log data. I suggest you could use azure storage explorer.
2.Generate the SAS url.
3.After created, you could copy the sas url.
4.Install azure cli.
5.Run below command:
Login-AzureRmAccount
$PropertiesObject = @{applicationLogs=@{azureTableStorage=@{level="Verbose";sasUrl="yourtableSASurl"}}}
Set-AzureRmResource -PropertyObject $PropertiesObject -ResourceGroupName "yourresourcegroupname" -ResourceType Microsoft.Web/sites/config -ResourceName "webappname/logs" -ApiVersion 2015-08-01 -Force
Then you could find your log message in the table.
But, We don't typically recommend using Tables for log data - it can result in the append only pattern which at scale doesn't work effectively for Table Storage.
More details, you could refer to this reply.